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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
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    <link:label id="lab_bsprt_RepurchaseFacilityMember_label_en-US" xlink:label="lab_bsprt_RepurchaseFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Facility [Member]</link:label>
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    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_019ff14a-1b49-7476-985a-d136978afb6d_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate UPB</link:label>
    <link:label id="lab_us-gaap_LoansReceivableHeldForSaleAmount_label_en-US" xlink:label="lab_us-gaap_LoansReceivableHeldForSaleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableHeldForSaleAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansReceivableHeldForSaleAmount"/>
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    <link:label id="lab_srt_MaximumMember_019ff14a-1b49-7396-880c-1a474c5aeb07_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019ff14a-1bcb-7b62-84e7-46a20876da78_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
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    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_019ff14a-1bcb-7514-99ce-14475981b49f_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Assets [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_019ff14a-1b49-7928-bf8d-5f1b865c25f1_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_019ff14a-1b49-7c15-92c8-b765b2cd2ce2_negatedNetLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Other than Temporary Impairments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtAmortizedCostOtherThanTemporaryImpairments"/>
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    <link:label id="lab_dei_Security12bTitle_019ff14a-1b48-7e14-ad50-d5b312586208_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
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    <link:label id="lab_us-gaap_SubsequentEventMember_019ff14a-1c3c-7dcb-9940-13d5ed7ce961_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019ff14a-1bcb-77c7-903c-e9481c5fae0b_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Amount</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019ff14a-1b49-7bbf-8e01-ceac66cbde60_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted net income/(loss) applicable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019ff14a-1bcb-7a00-82af-abcb5470be61_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
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    <link:label id="lab_bsprt_December2021MultifamilyMember_label_en-US" xlink:label="lab_bsprt_December2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">December 2021 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_December2021MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_December2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">December 2021 Multifamily</link:label>
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    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueOtherChangesThatAffectBalanceAmount_019ff14a-1b49-7977-b72f-160a5c7366ba_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueOtherChangesThatAffectBalanceAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepayments and write-offs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedValueOtherChangesThatAffectBalanceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtAmortizedValueOtherChangesThatAffectBalanceAmount"/>
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    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
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    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_019ff14a-1c3b-7eab-84a6-984a5822c5ac_terseLabel_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jeffersonville, GA</link:label>
    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_label_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jeffersonville, Georgia [Member]</link:label>
    <link:label id="lab_bsprt_JeffersonvilleGeorgiaMember_documentation_en-US" xlink:label="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jeffersonville, Georgia</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JeffersonvilleGeorgiaMember" xlink:href="bsprt-20260930.xsd#bsprt_JeffersonvilleGeorgiaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JeffersonvilleGeorgiaMember" xlink:to="lab_bsprt_JeffersonvilleGeorgiaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_019ff14a-1bcb-77a9-be5d-b0fb01956680_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Charge offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff (Recovery)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusAxis_019ff14a-1b49-797a-9524-4e0ffe32badb_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusAxis_label_en-US" xlink:label="lab_us-gaap_PledgedStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgedStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusAxis" xlink:to="lab_us-gaap_PledgedStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019ff14a-1b48-7c3a-bebb-8884421bcf8c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateLineItems_019ff14a-1bcb-7258-9afa-af0802393ac1_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:label id="lab_us-gaap_RealEstateLineItems_label_en-US" xlink:label="lab_us-gaap_RealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateLineItems" xlink:to="lab_us-gaap_RealEstateLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_019ff14a-1aa9-75bf-83c5-7783c6faab27_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TypeOfReserveDomain_019ff14a-1b49-76ea-b7dc-50c6c7179a84_terseLabel_en-US" xlink:label="lab_srt_TypeOfReserveDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Type of Reserve [Domain]</link:label>
    <link:label id="lab_srt_TypeOfReserveDomain_label_en-US" xlink:label="lab_srt_TypeOfReserveDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Type of Reserve [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TypeOfReserveDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_TypeOfReserveDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TypeOfReserveDomain" xlink:to="lab_srt_TypeOfReserveDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019ff14a-1bcb-72c6-9a5e-7a29f735a79e_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Expected Amortization of MSRs</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019ff14a-1bcb-7f5e-b028-1585d16046fe_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Expected Future Amortization Expense</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, and Capitalized Cost, Software to be Sold, Leased, or Marketed, Estimated Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_019ff14a-1b48-70c4-8752-01a316fe113d_periodStartLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_019ff14a-1b48-7ca8-8775-4e7dbf47f928_periodEndLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_019ff14a-1bcb-7632-99e8-847e53dd807d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_019ff14a-1c3c-7368-b226-b5d8b235a563_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor obligations, maximum exposure, undiscounted</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsMaximumExposure_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Maximum Exposure, Undiscounted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsMaximumExposure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuaranteeObligationsMaximumExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsMaximumExposure" xlink:to="lab_us-gaap_GuaranteeObligationsMaximumExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet_019ff14a-1c3b-7357-9fee-e3f76dfa93a1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accretion of deferred commitment fees</link:label>
    <link:label id="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet_label_en-US" xlink:label="lab_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Deferred Loan Origination Fees, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfDeferredLoanOriginationFeesNet"/>
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    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_019ff14a-1bcb-7675-bb61-8c2e2a5a938b_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019ff14a-1b49-7835-bda9-516dd2d6f3ed_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_019ff14a-1aa9-7318-b501-ea9d648ea619_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost by Year of Origination</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss, by Origination Year [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLossByOriginationYearAbstract"/>
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    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_019ff14a-1aa9-79de-9d5f-8d31f14c8293_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing asset at fair value, amount</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtFairValueAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome_019ff14a-1c3c-7b7b-87eb-cf31f31e872c_negatedTerseLabel_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in net assets of consolidated variable interest entity, CMBS trust</link:label>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome_label_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Net Assets Of Variable Interest Entity, CMBS Trust, Non-Cash Income</link:label>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome_documentation_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Net Assets Of Variable Interest Entity, CMBS Trust, Non-Cash Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:href="bsprt-20260930.xsd#bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:to="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrustNonCashIncome" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsMarketableSecurities"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_019ff14a-1b48-7154-947c-a205686054d3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019ff14a-1b48-7ff3-ad85-ffeb977661d2_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesAxis"/>
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    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_019ff14a-1bcb-7670-a66d-83e766866943_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock shares repurchased, average price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_019ff14a-1bcb-7cc5-ae49-a4fa36e36501_netLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net average purchase price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_label_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Acquired, Average Cost Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
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    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019ff14a-1b49-7109-a299-8aa22ba30b50_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain_019ff14a-1bcb-7680-8f3b-ec88d1237cae_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentPerformanceStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:to="lab_us-gaap_FinancialInstrumentPerformanceStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DevelopedTechnologyRightsMember_019ff14a-1bcb-77fe-95a5-77c630fdf29a_terseLabel_en-US" xlink:label="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Developed Technology Rights</link:label>
    <link:label id="lab_us-gaap_DevelopedTechnologyRightsMember_label_en-US" xlink:label="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Developed Technology Rights [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DevelopedTechnologyRightsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DevelopedTechnologyRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DevelopedTechnologyRightsMember" xlink:to="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_019ff14a-1b49-710a-8f6d-63bdfec6aeb9_totalLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned, net</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Net</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentNet_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedHeldForInvestmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:to="lab_bsprt_RealEstateOwnedHeldForInvestmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust_019ff14a-1c3c-76b0-8cfc-9fece8cd9c2a_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans acquired via consolidated VIE CMBS trust</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage loans Acquired, VIE CMBS Trust</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage loans Acquired, VIE CMBS Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansAcquiredVIECMBSTrust"/>
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    <link:label id="lab_bsprt_NewEnglandMember_019ff14a-1bcb-7429-8a6f-c41ad7756c83_terseLabel_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New England</link:label>
    <link:label id="lab_bsprt_NewEnglandMember_label_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New England [Member]</link:label>
    <link:label id="lab_bsprt_NewEnglandMember_documentation_en-US" xlink:label="lab_bsprt_NewEnglandMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">New England</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewEnglandMember" xlink:href="bsprt-20260930.xsd#bsprt_NewEnglandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewEnglandMember" xlink:to="lab_bsprt_NewEnglandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_019ff14a-1bcb-794d-8bb0-e070deeefe39_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense</link:label>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_label_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentForAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentForAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentForAmortization" xlink:to="lab_us-gaap_AdjustmentForAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_019ff14a-1b48-7d1b-a4de-7b9dc6cb1c9d_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Loans in pool</link:label>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_label_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral, Number Of Mortgage Assets</link:label>
    <link:label id="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral, Number of Mortgage Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:href="bsprt-20260930.xsd#bsprt_DebtInstrumentCollateralNumberOfMortgageAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:to="lab_bsprt_DebtInstrumentCollateralNumberOfMortgageAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_October2022MultifamilyMember_019ff14a-1c3b-78c8-9995-7764756443d6_terseLabel_en-US" xlink:label="lab_bsprt_October2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">October 2022 Multifamily</link:label>
    <link:label id="lab_bsprt_October2022MultifamilyMember_label_en-US" xlink:label="lab_bsprt_October2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">October 2022 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_October2022MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_October2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">October 2022 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_October2022MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_October2022MultifamilyMember"/>
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    <link:label id="lab_us-gaap_LeasesAbstract_019ff14a-1bcb-777e-8ea3-30a68964ce27_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019ff14a-1b48-7f5b-9de6-8a787cd0155c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions and Arrangements</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
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    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_01a0677b-154d-767d-bcd0-5dad097f5847_terseLabel_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property transferred from real estate owned, held for investment to real estate owned, held for sale</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_label_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Sale</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale_documentation_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForSale"/>
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    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019ff14a-1b49-7ef4-8788-d4c4c17607f4_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
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    <link:label id="lab_us-gaap_PaymentsToMinorityShareholders_019ff14a-1bcb-74d6-844a-c75ff204ed80_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions to non-controlling interest</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToMinorityShareholders" xlink:to="lab_us-gaap_PaymentsToMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating3Member_019ff14a-1b48-7530-a667-3540ef728cca_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3</link:label>
    <link:label id="lab_bsprt_InvestmentRating3Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 3 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating3Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating3Member" xlink:href="bsprt-20260930.xsd#bsprt_InvestmentRating3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating3Member" xlink:to="lab_bsprt_InvestmentRating3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_019ff14a-1bcb-7d15-b4da-d934947cab5f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate owned, held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:to="lab_us-gaap_ProceedsFromSaleOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_019ff14a-1b49-7796-bdff-5092e6f3ed90_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestOriginatedMoreThanFiveYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019ff14a-1b49-7814-91de-e61e9853f621_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_019ff14a-1b49-70f7-bf4a-b2d5c481cf8a_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_019ff14a-1aa8-7e89-b316-1b2102ea4b7c_negatedLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Premium amortization and (discount accretion), net</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_019ff14a-1bcb-76b3-b636-95c5d38a6d2d_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Pledged assets</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_019ff14a-1bcb-754e-82ef-655952034846_netLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Principal Balance of Collateralized Mortgage Assets</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:to="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019ff14a-1bcb-78b7-a4ad-f690c226e1d8_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_019ff14a-1aa9-78a7-a2ec-f73816764dc7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, held to maturity</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_019ff14a-1aa9-7f11-9c40-0dfe5901a1d9_terseLabel_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit</link:label>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_FifthThirdWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fifth Third WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FifthThirdWHLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_FifthThirdWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FifthThirdWHLineOfCreditMember" xlink:to="lab_bsprt_FifthThirdWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedSalaries_019ff14a-1b48-764b-a2a9-bbfdd513a5b6_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedSalaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedSalaries_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedSalaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Salaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedSalaries" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedSalaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedSalaries" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedSalaries" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate_019ff14a-1bcb-7594-ae39-c892cafed0b5_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Interest Rate</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Weighted Average Interest Rate</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_019ff14a-1aa9-76c9-8702-2ca119ee6ef9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets at Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_019ff14a-1c3b-75b9-adc0-f49a3bb2e8b5_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-7700-a819-b69389eb987a_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-7001-a024-b8cd0310ed0a_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-7482-b151-34025ed79fbe_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost basis</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember_019ff14a-1b48-7916-a98c-e7dae7fa72c3_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019ff14a-1b49-7a0f-bd08-038e5adddaf0_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_019ff14a-1bcb-735a-b31f-356460fb4ca6_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansMember" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageLoansMember" xlink:to="lab_bsprt_CommercialMortgageLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest_019ff14a-1bcb-7457-9459-a03e52d4b52a_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) before taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss), Including Portion Attributable to Noncontrolling Interest, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_019ff14a-1b49-73a0-ac49-da5c996c21e1_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_019ff14a-1bcb-78c3-8d88-841d81f80376_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019ff14a-1b48-7c2d-90bb-fb08780202a4_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity_019ff14a-1bcb-7d8b-983f-742f2d6b28ff_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Monthly asset management fee (percent)</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Monthly Asset Management Fee, Percent Of Stockholders' Equity</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Monthly Asset Management Fee, Percent of Stockholders' Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:href="bsprt-20260930.xsd#bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:to="lab_bsprt_RelatedPartyTransactionMonthlyAssetManagementFeePercentOfStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019ff14a-1b49-75a4-b880-4a14cb35e037_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_019ff14a-1bcb-7100-847d-dc8631a21f44_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Return of capital from equity method investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_label_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution, Return of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:to="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorLoansMember_019ff14a-1aa9-79ea-99d2-e411a3dea4c4_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior loans</link:label>
    <link:label id="lab_us-gaap_SeniorLoansMember_label_en-US" xlink:label="lab_us-gaap_SeniorLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorLoansMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeniorLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorLoansMember" xlink:to="lab_us-gaap_SeniorLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable_019ff14a-1b48-7bb0-9f76-3cc3a4804073_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Interest Receivable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Accrued Interest Receivable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Accrued Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredAccruedInterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019ff14a-1aa8-7572-9b6a-c29528d850f6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level II</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019ff14a-1aa9-7b8e-b7a6-5e51a1bfb80c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_019ff14a-1b49-734f-bba3-bcc9b15d4c8f_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedThreeYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_019ff14a-1b49-7650-9a74-f6278de4fbb5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 or more days past due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesRevenueNetMember_019ff14a-1bcb-7099-adcb-10aa44b954fb_terseLabel_en-US" xlink:label="lab_us-gaap_SalesRevenueNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Benchmark</link:label>
    <link:label id="lab_us-gaap_SalesRevenueNetMember_label_en-US" xlink:label="lab_us-gaap_SalesRevenueNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesRevenueNetMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesRevenueNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesRevenueNetMember" xlink:to="lab_us-gaap_SalesRevenueNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_019ff14a-1b48-77a9-b703-fd471991a1ca_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale or repayment of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale, Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_019ff14a-1b48-76a4-bd25-2ae8302e9f77_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019ff14a-1b49-7b26-a3df-ad73938cf69f_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019ff14a-1bcb-7769-bf63-73daa6aed1df_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019ff14a-1bcb-7c2e-9f3c-8646ef3140a9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operations by Segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AtTheMarketOfferingProgramMember_019ff14a-1b49-7273-9ecf-0cc9b15e5661_terseLabel_en-US" xlink:label="lab_bsprt_AtTheMarketOfferingProgramMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">At-the-Market Offering Program</link:label>
    <link:label id="lab_bsprt_AtTheMarketOfferingProgramMember_label_en-US" xlink:label="lab_bsprt_AtTheMarketOfferingProgramMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">At-the-Market Offering Program [Member]</link:label>
    <link:label id="lab_bsprt_AtTheMarketOfferingProgramMember_documentation_en-US" xlink:label="lab_bsprt_AtTheMarketOfferingProgramMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">At-the-Market Offering Program</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AtTheMarketOfferingProgramMember" xlink:href="bsprt-20260930.xsd#bsprt_AtTheMarketOfferingProgramMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AtTheMarketOfferingProgramMember" xlink:to="lab_bsprt_AtTheMarketOfferingProgramMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral_019ff14a-1bcb-739d-a465-54a63442e9b4_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged investment securities</link:label>
    <link:label id="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral_label_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Loaned, Fair Value of Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesLoanedFairValueOfCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:to="lab_us-gaap_SecuritiesLoanedFairValueOfCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_019ff14a-1aa9-7445-a421-0d6c69b4b4eb_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019ff14a-1bcb-7f9e-b2cd-c1d917ff7008_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherGeneralIncomeExpense_01a164da-bdce-7fc8-af68-b1cbb05023a0_verboseLabel_en-US" xlink:label="lab_bsprt_OtherGeneralIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other related party expenses</link:label>
    <link:label id="lab_bsprt_OtherGeneralIncomeExpense_label_en-US" xlink:label="lab_bsprt_OtherGeneralIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General Income (Expense)</link:label>
    <link:label id="lab_bsprt_OtherGeneralIncomeExpense_documentation_en-US" xlink:label="lab_bsprt_OtherGeneralIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other General Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherGeneralIncomeExpense" xlink:href="bsprt-20260930.xsd#bsprt_OtherGeneralIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherGeneralIncomeExpense" xlink:to="lab_bsprt_OtherGeneralIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019ff14a-1b49-79d7-b3bb-fff4c5b594f8_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lessee, Operating Lease, Liability, to be Paid, Maturity</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
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    <link:label id="lab_us-gaap_LossContingencyDisclosures_019ff14a-1bcb-77af-a102-7dd0aaba0499_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyDisclosures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Loss Sharing</link:label>
    <link:label id="lab_us-gaap_LossContingencyDisclosures_label_en-US" xlink:label="lab_us-gaap_LossContingencyDisclosures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyDisclosures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyDisclosures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyDisclosures" xlink:to="lab_us-gaap_LossContingencyDisclosures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_019ff14a-1c3b-7872-a553-0a4f6173cc80_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of non - cash flow information:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7794-94ef-7c170c948d10_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7adc-8895-ad0f5ec675df_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7e5c-8822-473df9224646_negatedPeriodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses, beginning of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-72c5-9daf-7f6e1112e973_negatedPeriodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses, end of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7bab-b940-288e0c5c58f2_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7b12-affb-29cd92151af0_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_019ff14a-1b49-7ea3-a448-9b58200f8937_negatedNetLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterest"/>
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    <link:label id="lab_dei_DocumentPeriodEndDate_019ff14a-1bcb-717b-9b98-d5f1d5102707_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019ff14a-1b49-7bd4-8d76-d4b7894eac1e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019ff14a-1b48-7921-a9ae-da49cea47141_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019ff14a-1b48-7296-aa97-ad34ea24691a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019ff14a-1b49-7ab3-9e3c-62aa23c1eea6_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019ff14a-1bcb-7af2-b715-0eba62ee30fb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate, effective percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_019ff14a-1aa9-7245-996e-e5410aac2c26_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions from non-controlling interest</link:label>
    <link:label id="lab_us-gaap_ProceedsFromMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromMinorityShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromMinorityShareholders" xlink:to="lab_us-gaap_ProceedsFromMinorityShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_019ff14a-1b48-7fed-a7f4-5b5823bfb692_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated performance fee, percent that total return exceeds per year</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Performance Fee Total Return Threshold</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Performance Fee Total Return Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:href="bsprt-20260930.xsd#bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:to="lab_bsprt_RelatedPartyTransactionSubordinatedPerformanceFeeTotalReturnThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_019ff14a-1aa9-7379-af3c-b6b386e8e751_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_019ff14a-1bcb-7a2f-aa16-a48578aa87c6_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_019ff14a-1bcb-7ea2-aed2-349a6972b745_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Sold under Agreements to Repurchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchase"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchase" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary_019ff14a-1b49-73b0-a894-bc3a6655cb1b_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnSecondAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019ff14a-1b49-76d2-9b2b-38e369638523_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019ff14a-1bcb-7528-85c2-d0029986a610_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_019ff14a-1aa9-7c45-a4f4-5229a57ded36_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of positions with gross unrealized (loss) gain period less than 12 months</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Gross Gain (Loss) Position, Number of Positions</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Unrealized Gross Gain (Loss) Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleUnrealizedGrossGainLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet_019ff14a-1bcb-713b-834d-3a4ab7787501_terseLabel_en-US" xlink:label="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet_label_en-US" xlink:label="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Granted, Value, Share-Based Payment Arrangement, after Forfeiture, Net</link:label>
    <link:label id="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet_documentation_en-US" xlink:label="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Granted, Value, Share-Based Payment Arrangement, after Forfeiture, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:href="bsprt-20260930.xsd#bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:to="lab_bsprt_SharesGrantedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_019ff14a-1b49-7936-9e86-2da1920a2a48_terseLabel_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum allowable share conversions per month (in shares)</link:label>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_label_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Maximum Allowed Share Conversions Per Month</link:label>
    <link:label id="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth_documentation_en-US" xlink:label="lab_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Maximum Allowed Share Conversions Per Month</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth" xlink:href="bsprt-20260930.xsd#bsprt_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesMaximumAllowedShareConversionsPerMonth"/>
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    <link:label id="lab_us-gaap_MortgagesMember_019ff14a-1bcb-7c7b-84d6-bedcca7b86b3_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_019ff14a-1bcb-7b8e-93b4-445dea109a00_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgagesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesMember" xlink:to="lab_us-gaap_MortgagesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019ff14a-1bcb-7b66-9753-f30fb623906f_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019ff14a-1bcb-712a-b2f2-90ad2f7ffe09_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesLineItems_019ff14a-1c3b-7d32-9fe1-448fe9081748_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Line Items]</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesLineItems_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesLineItems" xlink:to="lab_us-gaap_OffsettingLiabilitiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WalgreensJVMember_019ff14a-1c3b-7d2b-9b82-528ae22470e4_terseLabel_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Walgreens JV</link:label>
    <link:label id="lab_bsprt_WalgreensJVMember_label_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Walgreens JV [Member]</link:label>
    <link:label id="lab_bsprt_WalgreensJVMember_documentation_en-US" xlink:label="lab_bsprt_WalgreensJVMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Walgreens JV</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WalgreensJVMember" xlink:href="bsprt-20260930.xsd#bsprt_WalgreensJVMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WalgreensJVMember" xlink:to="lab_bsprt_WalgreensJVMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019ff14a-1bcb-7226-bf73-33fe8b969103_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseIncome_019ff14a-1bcb-7b8c-b226-d43970f75855_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from real estate owned</link:label>
    <link:label id="lab_us-gaap_LeaseIncome_label_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseIncome" xlink:to="lab_us-gaap_LeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_019ff14a-1b48-705a-9864-afe0bf61e777_terseLabel_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility</link:label>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_ChurchillRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_ChurchillRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Churchill Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChurchillRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_ChurchillRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChurchillRepoFacilityMember" xlink:to="lab_bsprt_ChurchillRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock_019ff14a-1b48-7bda-902a-70785431675d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Activity Related to MSRs</link:label>
    <link:label id="lab_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock" xlink:to="lab_us-gaap_ScheduleOfServicingAssetsAtAmortizedValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019ff14a-1bcb-7745-a680-880e7cb9d367_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019ff14a-1bcb-728e-8e86-307050221098_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019ff14a-1b49-7069-a85e-e2f9d481c9a6_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis_01a16140-8a02-7c77-9a50-7d19d7b94699_terseLabel_en-US" xlink:label="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Partner Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis_label_en-US" xlink:label="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partner Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnerTypeOfPartnersCapitalAccountAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:to="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019ff14a-1b49-7d50-895b-a3950638d86e_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Real estate securities, available for sale, measured at fair value, amortized cost of $0 and $151,946 as of September 30, 2026 and December 31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019ff14a-1b49-7591-9f97-b9405093052b_netLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_019ff14a-1b49-78c5-9209-558b0e9fb25d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate securities, available for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Excluding Accrued Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward_019ff14a-1bcb-7f7b-8fe6-dca2cb32c3d9_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_019ff14a-1c3b-7ac9-bd69-9737076183bd_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Servicing revenue, net</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_019ff14a-1c3b-7353-89b2-5e46934455c5_totalLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total servicing revenue, net</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_019ff14a-1c3b-7842-be6b-5f9495a390ae_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing revenue</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fee, Late Fee, and Ancillary Fee Earned in Exchange for Servicing Financial Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:to="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_019ff14a-1b49-7b6e-b956-cc1ec531b877_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allocation of the Purchase Consideration</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_019ff14a-1aa9-78f0-b2eb-ca927aec9bfd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of real estate securities, available for sale</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_019ff14a-1b48-7921-8464-e252c9138daa_terseLabel_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of stock, preferred stock to common stock, notice period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_label_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock To Common Stock, Notice Period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod_documentation_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock To Common Stock, Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:href="bsprt-20260930.xsd#bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:to="lab_bsprt_ConversionOfStockPreferredStockToCommonStockNoticePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList_019ff14a-1b49-7474-8717-bf91a71fa930_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseIncomeComprehensiveIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_019ff14a-1bcb-7257-8c22-c7b53c4777dc_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_019ff14a-1bcb-7b6a-82f7-faa50c4cd70e_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_019ff14a-1bcb-7714-b099-662664ab1d46_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDeposits" xlink:to="lab_us-gaap_InterestExpenseDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTable_019ff14a-1b48-7000-8a4c-9782e4a48b5d_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table]</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTable_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTable" xlink:to="lab_us-gaap_OffsettingLiabilitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_019ff14a-1aa9-740f-b4c9-1fe7e1754a79_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskLineItems_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskLineItems" xlink:to="lab_us-gaap_ConcentrationRiskLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusAxis_019ff14a-1b49-7ee4-b29a-75f2cc3b509f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentPerformanceStatusAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentPerformanceStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument Performance Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentPerformanceStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentPerformanceStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentPerformanceStatusAxis" xlink:to="lab_us-gaap_FinancialInstrumentPerformanceStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DenominatorAbstract_019ff14a-1bcb-7aae-91a5-d96006e593ad_terseLabel_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator</link:label>
    <link:label id="lab_bsprt_DenominatorAbstract_label_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Denominator [Abstract]</link:label>
    <link:label id="lab_bsprt_DenominatorAbstract_documentation_en-US" xlink:label="lab_bsprt_DenominatorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Denominator [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DenominatorAbstract" xlink:href="bsprt-20260930.xsd#bsprt_DenominatorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DenominatorAbstract" xlink:to="lab_bsprt_DenominatorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_019ff14a-1c3b-75f0-bd12-a5bb551f5d84_terseLabel_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing obligations, allowance</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_label_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowance_documentation_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsAllowance" xlink:href="bsprt-20260930.xsd#bsprt_LossSharingObligationsAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossSharingObligationsAllowance" xlink:to="lab_bsprt_LossSharingObligationsAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_019ff14a-1bcb-7075-b45c-cacecf971b4f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year one, originated in current fiscal year</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PartnersCapitalAccountDistributionPercentage_01a1613f-14b4-744f-8f98-87ebcb915411_terseLabel_en-US" xlink:label="lab_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Partners capital account distribution percentage</link:label>
    <link:label id="lab_bsprt_PartnersCapitalAccountDistributionPercentage_label_en-US" xlink:label="lab_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners Capital Account Distribution Percentage</link:label>
    <link:label id="lab_bsprt_PartnersCapitalAccountDistributionPercentage_documentation_en-US" xlink:label="lab_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Partners Capital Account Distribution Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:href="bsprt-20260930.xsd#bsprt_PartnersCapitalAccountDistributionPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:to="lab_bsprt_PartnersCapitalAccountDistributionPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019ff14a-1bcb-7db8-9ac8-3b309e3de0c0_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_019ff14a-1aa9-7b90-baf0-26d331279018_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_019ff14a-1aa9-7915-942f-56de6c24d505_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019ff14a-1bcb-799e-84ab-6d034cb6096c_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_019ff14a-1b48-7784-9793-643d916a1cca_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common dividends paid (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_019ff14a-1b48-7a23-a41c-62d4a25ae2af_terseLabel_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt</link:label>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_label_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt [Member]</link:label>
    <link:label id="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember_documentation_en-US" xlink:label="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fee to Acquire and Originate Real Estate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:href="bsprt-20260930.xsd#bsprt_FeetoAcquireandOriginateRealEstateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:to="lab_bsprt_FeetoAcquireandOriginateRealEstateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_019ff14a-1aa9-75f9-af21-2a232c76eac6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers out of Level III</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers out of Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityTable_019ff14a-1b48-7dd8-8f2e-f92d3d4e1fd6_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Table]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityTable_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityTable" xlink:to="lab_us-gaap_LineOfCreditFacilityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_019ff14a-1aa8-7ef3-a004-00c0e45819b3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions declared</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_019ff14a-1c3b-7ba0-9021-9728dc793a97_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_019ff14a-1c3b-7b90-9fbb-ed5f4761f91d_verboseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Distribution payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_019ff14a-1aa9-7ace-83dd-6fa71eb3032e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, expected tax deductible</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Goodwill, Expected Tax Deductible, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:to="lab_us-gaap_BusinessAcquisitionPurchasePriceAllocationGoodwillExpectedTaxDeductibleAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CMBSBondsMember_019ff14a-1aa8-7de1-9229-9d13e39eff0b_terseLabel_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:label id="lab_bsprt_CMBSBondsMember_label_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CMBS Bonds [Member]</link:label>
    <link:label id="lab_bsprt_CMBSBondsMember_documentation_en-US" xlink:label="lab_bsprt_CMBSBondsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CMBSBondsMember" xlink:href="bsprt-20260930.xsd#bsprt_CMBSBondsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CMBSBondsMember" xlink:to="lab_bsprt_CMBSBondsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember_019ff14a-1bcb-7503-8897-c437926dc241_terseLabel_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition fees and expenses, amount capitalized</link:label>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember_label_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition Fees And Expenses, Amount Capitalized [Member]</link:label>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember_documentation_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Fees And Expenses, Amount Capitalized [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:href="bsprt-20260930.xsd#bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:to="lab_bsprt_AcquisitionFeesAndExpensesAmountCapitalizedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019ff14a-1bcb-73fc-83da-05c1bd7e2ded_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Carried at Fair Value on a Recurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_019ff14a-1b49-7eba-8f14-6335164524d0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIntangibleAssetsMember" xlink:to="lab_us-gaap_OtherIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansAtFairValueMember_019ff14a-1c3b-7f25-8092-9a65869500d2_verboseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">VIE assets, measured at fair value(1)</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansAtFairValueMember_019ff14a-1c3b-70db-b1c5-b3aa2116b654_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CML, at fair value</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansAtFairValueMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, At Fair Value [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansAtFairValueMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:to="lab_bsprt_CommercialMortgageLoansAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_019ff14a-1aa9-7f7c-b6af-2bdad978153b_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash outflows from operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_019ff14a-1b49-7ec1-a4fb-31b18dad1bd8_terseLabel_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible lease assets</link:label>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_label_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Lease Assets [Member]</link:label>
    <link:label id="lab_bsprt_IntangibleLeaseAssetsMember_documentation_en-US" xlink:label="lab_bsprt_IntangibleLeaseAssetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Intangible Lease Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_IntangibleLeaseAssetsMember" xlink:href="bsprt-20260930.xsd#bsprt_IntangibleLeaseAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_IntangibleLeaseAssetsMember" xlink:to="lab_bsprt_IntangibleLeaseAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019ff14a-1bcb-7876-acc5-7649c90e7f2f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level I</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareDevelopmentMember_019ff14a-1bcb-765c-85b7-cb077b6d80bc_terseLabel_en-US" xlink:label="lab_us-gaap_SoftwareDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software development</link:label>
    <link:label id="lab_us-gaap_SoftwareDevelopmentMember_label_en-US" xlink:label="lab_us-gaap_SoftwareDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software, Internally Developed [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareDevelopmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareDevelopmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareDevelopmentMember" xlink:to="lab_us-gaap_SoftwareDevelopmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_019ff14a-1bcb-7816-9955-72326e6ab523_terseLabel_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor</link:label>
    <link:label id="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock_label_en-US" xlink:label="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedules of Concentration of Risk, by Risk Factor [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:to="lab_us-gaap_SchedulesOfConcentrationOfRiskByRiskFactorTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_019ff14a-1aa9-739b-a3d1-6f14a2fdff12_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) from commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Financing Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfNotesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:to="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_019ff14a-1bcb-7344-ad9c-11c8a55586a7_negatedTerseLabel_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination and purchase of commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_label_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Origination And Purchase Of Commercial Mortgage Loans, Held For Sale</link:label>
    <link:label id="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale_documentation_en-US" xlink:label="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Origination And Purchase Of Commercial Mortgage Loans, Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:to="lab_bsprt_OriginationAndPurchaseOfCommercialMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanMortgageObligationsFairValueDisclosure_019ff14a-1c3b-79ce-8e82-9fca6265d5f7_terseLabel_en-US" xlink:label="lab_bsprt_LoanMortgageObligationsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage-backed securities, at fair value</link:label>
    <link:label id="lab_bsprt_LoanMortgageObligationsFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_LoanMortgageObligationsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage Obligations, Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_LoanMortgageObligationsFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_LoanMortgageObligationsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan, Mortgage Obligations, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanMortgageObligationsFairValueDisclosure" xlink:href="bsprt-20260930.xsd#bsprt_LoanMortgageObligationsFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Financing Receivable [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarningsSaleOfCommercialMortgageLoanHeldForSale"/>
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    <link:label id="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember_019ff14a-1bcb-724e-abff-15bb6972c077_terseLabel_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableEliminatedInConsolidationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Eliminated in Consolidation</link:label>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019ff14a-1b48-7cab-9a35-10d198def5c1_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_srt_ScenarioUnspecifiedDomain_019ff14a-1bcb-7325-b541-5c63bfec3912_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioUnspecifiedDomain" xlink:to="lab_srt_ScenarioUnspecifiedDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019ff14a-1b49-7285-9c73-b164a8044d22_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
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    <link:label id="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain_01a16140-8a02-729a-a662-53ea274744ec_terseLabel_en-US" xlink:label="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Partner Type of Partners' Capital Account, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain_label_en-US" xlink:label="lab_us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partner Type of Partners' Capital Account, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnerTypeOfPartnersCapitalAccountNameDomain"/>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019ff14a-1b48-7a90-b20c-98cfeeb23f00_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, ROU</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019ff14a-1aa9-756f-9ad8-e80e075771ca_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_019ff14a-1bcb-7e32-942d-b646a05129f3_negatedTerseLabel_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Mortgage banking activities</link:label>
    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_label_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Loss On Mortgage Banking Activities Net</link:label>
    <link:label id="lab_bsprt_GainLossOnMortgageBankingActivitiesNet_documentation_en-US" xlink:label="lab_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain Loss On Mortgage Banking Activities Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GainLossOnMortgageBankingActivitiesNet" xlink:href="bsprt-20260930.xsd#bsprt_GainLossOnMortgageBankingActivitiesNet"/>
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    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_019ff14a-1bcb-7270-bc60-29576a99db8b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019ff14a-1bcb-715c-a99e-957ea6073c98_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_019ff14a-1bcb-738d-9f85-5524de3dea97_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Cash</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Cash</link:label>
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    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_019ff14a-1bcb-73c2-b731-84975ef0e15a_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Securities</link:label>
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    <link:label id="lab_us-gaap_LineOfCredit_019ff14a-1bcb-7608-92f5-f73ad5da4fd9_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount Outstanding</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateTable_019ff14a-1aa9-71ed-98e1-93dae244c5fc_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:label id="lab_us-gaap_RealEstateTable_label_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateTable" xlink:to="lab_us-gaap_RealEstateTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ff14a-1bcb-75a1-b905-14d6b12125a1_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ff14a-1bcb-71b3-b1b5-6367371861f6_periodStartLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Restricted cash, beginning of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ff14a-1bcb-7006-a553-4eebf2539ec0_periodEndLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Restricted cash, end of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_01a164c4-fc08-7eb4-a10b-265aba2cc711_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeAssetNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ff14a-1b49-71c6-9fc7-9884f29764b1_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ff14a-1b49-7c95-8bb9-ef838efdbc70_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_019ff14a-1b49-721a-9b50-cee4f52a0edf_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_019ff14a-1aa9-79d2-bdd2-a22ec7309f35_terseLabel_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_label_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC [Member]</link:label>
    <link:label id="lab_bsprt_NewPointHoldingsJVLLCMember_documentation_en-US" xlink:label="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NewPoint Holdings JV LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewPointHoldingsJVLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_NewPointHoldingsJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewPointHoldingsJVLLCMember" xlink:to="lab_bsprt_NewPointHoldingsJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_019ff14a-1b49-7d9b-98b5-85ac1b5d7426_terseLabel_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonrelated Party</link:label>
    <link:label id="lab_us-gaap_NonrelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_NonrelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonrelated Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrelatedPartyMember" xlink:to="lab_us-gaap_NonrelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedMember_019ff14a-1b48-7126-8a7a-14494af56d17_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedMember_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedMember" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedMember" xlink:to="lab_bsprt_RealEstateOwnedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_AffiliatedEntityMember_019ff14a-1c3b-7f17-a3b5-1a7bf418d39e_terseLabel_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affiliated Entity</link:label>
    <link:label id="lab_srt_AffiliatedEntityMember_label_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affiliated Entity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AffiliatedEntityMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_AffiliatedEntityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_AffiliatedEntityMember" xlink:to="lab_srt_AffiliatedEntityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_019ff14a-1b49-7ac3-a419-89d3fe0b0d41_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing under the DUS program</link:label>
    <link:label id="lab_us-gaap_LossContingencyEstimateOfPossibleLoss_label_en-US" xlink:label="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Estimate of Possible Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyEstimateOfPossibleLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:to="lab_us-gaap_LossContingencyEstimateOfPossibleLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_019ff14a-1b49-7af2-873a-6f32fd2989b0_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and Improvements</link:label>
    <link:label id="lab_us-gaap_BuildingAndBuildingImprovementsMember_label_en-US" xlink:label="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building and Building Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BuildingAndBuildingImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="lab_us-gaap_BuildingAndBuildingImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebt_019ff14a-1bcb-7b4a-ab2b-68d34bfc0a4e_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebt" xlink:to="lab_us-gaap_UnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeTable_019ff14a-1b48-7b6c-9073-d8f414ab1c4f_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeTable" xlink:to="lab_us-gaap_DerivativeTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_019ff14a-1bcb-74cf-ab89-5ca3c286e1f9_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specific allowance for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_019ff14a-1bcb-799e-8a58-6bffcba3b047_netLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Specific (provision)/benefit for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_019ff14a-1bcb-75e3-a2d1-3c73caaef6c9_verboseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Specific Allowance for Credit Losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_label_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Specific [Member]</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossSpecificMember_documentation_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossSpecificMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Specific</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForCreditLossSpecificMember" xlink:href="bsprt-20260930.xsd#bsprt_AllowanceForCreditLossSpecificMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfProductInformationTable_019ff14a-1bcb-7a74-99e7-396cafee7fd5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfProductInformationTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfProductInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operation, Product Information, Concentration of Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfProductInformationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfProductInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfProductInformationTable" xlink:to="lab_us-gaap_ScheduleOfProductInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019ff14a-1aa9-7d2d-8277-724b62b4fd26_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019ff14a-1bcb-7e20-9833-04bb537cb5d7_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_019ff14a-1b48-7513-9751-86401f23e73f_terseLabel_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Master repurchase agreements maturity (days)</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_label_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreements, Maturity Term</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm_documentation_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreements, Maturity Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:href="bsprt-20260930.xsd#bsprt_MasterRepurchaseAgreementsMaturityTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:to="lab_bsprt_MasterRepurchaseAgreementsMaturityTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_019ff14a-1b48-7460-9d0a-efee14f0ef79_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock_019ff14a-1c3b-7e13-b508-0f473468b640_terseLabel_en-US" xlink:label="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Assets and Liabilities</link:label>
    <link:label id="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock_label_en-US" xlink:label="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets And Liabilities [Text Block]</link:label>
    <link:label id="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock_documentation_en-US" xlink:label="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Offsetting Assets and Liabilities [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_OffsettingAssetsAndLiabilitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:to="lab_bsprt_OffsettingAssetsAndLiabilitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_019ff14a-1b49-73a5-9810-c0950504631d_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating4Member_019ff14a-1b48-73f6-82e7-70f4491a3d63_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">4</link:label>
    <link:label id="lab_bsprt_InvestmentRating4Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 4 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating4Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 4 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating4Member" xlink:href="bsprt-20260930.xsd#bsprt_InvestmentRating4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating4Member" xlink:to="lab_bsprt_InvestmentRating4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019ff14a-1b48-7963-82a1-5b06a3b373ef_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_019ff14a-1b49-7215-9d36-fc7bee26be51_terseLabel_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC</link:label>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_label_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC [Member]</link:label>
    <link:label id="lab_bsprt_GarfieldPGJVHoldCoLLCMember_documentation_en-US" xlink:label="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Garfield PG JV HoldCo LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_GarfieldPGJVHoldCoLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:to="lab_bsprt_GarfieldPGJVHoldCoLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_019ff14a-1bcb-75cb-b0d5-4ac4a5634572_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Removal of non-performing loan amortized cost</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Removal Of Carrying Value</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Removal Of Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualRemovalOfCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBankingAbstract_label_en-US" xlink:label="lab_us-gaap_MortgageBankingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Banking [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBankingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageBankingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBankingAbstract" xlink:to="lab_us-gaap_MortgageBankingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_019ff14a-1b49-70db-bc6a-ea4aa2666a1d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_019ff14a-1b49-7095-94c0-0d06946b78dd_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockMember_019ff14a-1b49-701a-ad33-7ca59a166e81_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertiblePreferredStockMember" xlink:to="lab_us-gaap_ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_U.S.BankNationalAssociationMember_019ff14a-1b48-78fc-b000-b53e365ee59c_terseLabel_en-US" xlink:label="lab_bsprt_U.S.BankNationalAssociationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Bank National Association</link:label>
    <link:label id="lab_bsprt_U.S.BankNationalAssociationMember_label_en-US" xlink:label="lab_bsprt_U.S.BankNationalAssociationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">U.S. Bank National Association [Member]</link:label>
    <link:label id="lab_bsprt_U.S.BankNationalAssociationMember_documentation_en-US" xlink:label="lab_bsprt_U.S.BankNationalAssociationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">U.S. Bank National Association and U.S. Bank National Association [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_U.S.BankNationalAssociationMember" xlink:href="bsprt-20260930.xsd#bsprt_U.S.BankNationalAssociationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_U.S.BankNationalAssociationMember" xlink:to="lab_bsprt_U.S.BankNationalAssociationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GreatLakesMember_019ff14a-1b48-7c10-af8a-34da2e80e18f_terseLabel_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Great Lakes</link:label>
    <link:label id="lab_bsprt_GreatLakesMember_label_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Great Lakes [Member]</link:label>
    <link:label id="lab_bsprt_GreatLakesMember_documentation_en-US" xlink:label="lab_bsprt_GreatLakesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Great Lakes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GreatLakesMember" xlink:href="bsprt-20260930.xsd#bsprt_GreatLakesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GreatLakesMember" xlink:to="lab_bsprt_GreatLakesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019ff14a-1b49-7b09-a2ee-771a9daa5172_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtMember_019ff14a-1c3b-71f1-9765-425b8d76f2fd_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_019ff14a-1b49-773e-926c-d29ef820543c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of and contributions to equity method investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019ff14a-1c3b-785e-a870-e2a55b5c9540_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate, stated percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019ff14a-1b48-741c-a6f8-1aaa9cd9ae1a_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_019ff14a-1b48-7481-a739-ad167ca8690f_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MortgageLoansOnRealEstateNamePropertyTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:to="lab_srt_MortgageLoansOnRealEstateNamePropertyTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019ff14a-1aa9-777f-9732-adf62ef2f270_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_019ff14a-1aa9-7a64-b313-06cdb6ad5301_netLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_019ff14a-1aa9-7bfe-8071-b7c2de58e804_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets, at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_019ff14a-1b48-76bc-ac00-ee5637c1c1d3_terseLabel_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_label_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Junior Debt [Member]</link:label>
    <link:label id="lab_bsprt_UnsecuredJuniorDebtMember_documentation_en-US" xlink:label="lab_bsprt_UnsecuredJuniorDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Junior Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnsecuredJuniorDebtMember" xlink:href="bsprt-20260930.xsd#bsprt_UnsecuredJuniorDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnsecuredJuniorDebtMember" xlink:to="lab_bsprt_UnsecuredJuniorDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019ff14a-1aa8-7355-b3bf-da5c0120effe_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity interest (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_019ff14a-1bcb-7dc9-9dd9-e38544b9f918_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note I</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_label_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note I, Maturing October 2035 [Member]</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note I, Maturing October 2035</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:href="bsprt-20260930.xsd#bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:to="lab_bsprt_JuniorSubordinatedNoteIMaturingOctober2035Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_019ff14a-1b49-79a7-9f55-cf847efa92da_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allocation by Risk Rating</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Credit Quality Indicators [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:to="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_019ff14a-1bcb-722d-8722-aaa388910b74_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsNonrecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Nonrecurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsNonrecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsNonrecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_019ff14a-1bcb-7d8d-aabe-04a68139c530_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Interest Payable</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfessionalFees_019ff14a-1aa9-734b-8752-ebbee1e23b9c_terseLabel_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional fees</link:label>
    <link:label id="lab_us-gaap_ProfessionalFees_label_en-US" xlink:label="lab_us-gaap_ProfessionalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfessionalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfessionalFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfessionalFees" xlink:to="lab_us-gaap_ProfessionalFees" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonperformingFinancingReceivableMember_019ff14a-1aa9-718e-b407-fbb9eb46ebc7_terseLabel_en-US" xlink:label="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonperforming Financial Instruments</link:label>
    <link:label id="lab_us-gaap_NonperformingFinancingReceivableMember_label_en-US" xlink:label="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonperforming Financial Instruments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonperformingFinancingReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonperformingFinancingReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonperformingFinancingReceivableMember" xlink:to="lab_us-gaap_NonperformingFinancingReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BSPTMOMasterJVLLCMember_01a0ed58-f7e1-7bd6-8481-88b58af9cb3b_terseLabel_en-US" xlink:label="lab_bsprt_BSPTMOMasterJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BSP TMO Master JV LLC</link:label>
    <link:label id="lab_bsprt_BSPTMOMasterJVLLCMember_label_en-US" xlink:label="lab_bsprt_BSPTMOMasterJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BSP TMO Master JV LLC [Member]</link:label>
    <link:label id="lab_bsprt_BSPTMOMasterJVLLCMember_documentation_en-US" xlink:label="lab_bsprt_BSPTMOMasterJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BSP TMO Master JV LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BSPTMOMasterJVLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_BSPTMOMasterJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BSPTMOMasterJVLLCMember" xlink:to="lab_bsprt_BSPTMOMasterJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_019ff14a-1aa9-72b9-9e11-e7dc4cfc1069_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablePortfolioSegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_019ff14a-1b48-7c53-87f1-183174a9466f_terseLabel_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Add: Net income/(loss) from non-controlling interest - OP Units</link:label>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_label_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income/(Loss) From Non-Controlling Interest - OP Units</link:label>
    <link:label id="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits_documentation_en-US" xlink:label="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income/(Loss) From Non-Controlling Interest - OP Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:href="bsprt-20260930.xsd#bsprt_NetIncomeLossFromNonControllingInterestOPUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:to="lab_bsprt_NetIncomeLossFromNonControllingInterestOPUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_019ff14a-1bcb-7b7a-a257-f479840ab406_terseLabel_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency loans</link:label>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_label_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non US Government Sponsored-Enterprise Insured Loans [Member]</link:label>
    <link:label id="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember_documentation_en-US" xlink:label="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non US Government Sponsored-Enterprise Insured Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:href="bsprt-20260930.xsd#bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:to="lab_bsprt_NonUSGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_019ff14a-1aa9-77e1-8f27-85768c5a4c01_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive securities excluded from computation (in shares)</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MideastMember_019ff14a-1bcb-7f51-86b7-5ccb8fe9b633_terseLabel_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mideast</link:label>
    <link:label id="lab_bsprt_MideastMember_label_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mideast [Member]</link:label>
    <link:label id="lab_bsprt_MideastMember_documentation_en-US" xlink:label="lab_bsprt_MideastMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mideast</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MideastMember" xlink:href="bsprt-20260930.xsd#bsprt_MideastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MideastMember" xlink:to="lab_bsprt_MideastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019ff14a-1aa9-7040-ab74-1717039e5e84_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_019ff14a-1b49-78bd-aec8-fe1df15a195d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019ff14a-1bcb-79da-911f-50df26391744_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_019ff14a-1b49-7d1e-b2df-eafb07ca7091_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity:</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity_019ff14a-1aa8-7f3c-8567-8d36ea662e9c_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Contractual Maturity (years)</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Weighted Average Contractual Maturity</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Weighted Average Contractual Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleWeightedAverageContractualMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_019ff14a-1bcb-77c0-a76c-ad6c8f7a621c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_019ff14a-1bcb-70da-80fa-f3bc51e6c35c_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_OtherCreditDerivativesMember_label_en-US" xlink:label="lab_us-gaap_OtherCreditDerivativesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Credit Derivatives [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCreditDerivativesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherCreditDerivativesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCreditDerivativesMember" xlink:to="lab_us-gaap_OtherCreditDerivativesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_019ff14a-1b49-7188-b92e-8c7db91d2a10_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_019ff14a-1c3b-7120-b82b-f5775d040e41_terseLabel_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:label id="lab_us-gaap_PledgingPurposeAxis_label_en-US" xlink:label="lab_us-gaap_PledgingPurposeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgingPurposeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgingPurposeAxis" xlink:to="lab_us-gaap_PledgingPurposeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019ff14a-1c3b-73c6-a211-b0903dbb1fea_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_019ff14a-1aa9-71ba-a684-b8335bba372d_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable and Accrued Expenses, Current</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable and Accrued Expenses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccountsPayableAndAccruedExpensesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019ff14a-1bcb-759f-9b6e-bdeb05345490_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019ff14a-1b49-79e0-8aad-9cb7068c8b15_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_019ff14a-1aa9-7417-a130-e5cba0a2bcd8_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividend rate percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_019ff14a-1bcb-79e7-b807-cfd29fb95ae3_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Commercial Mortgage Loans Held for Investment Activity</link:label>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_label_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Notes Receivable Rollforward [Table Text Block]</link:label>
    <link:label id="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Notes Receivable Rollforward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateNotesReceivableRollforwardTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:to="lab_bsprt_RealEstateNotesReceivableRollforwardTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ClassAUnitsMember_019ff14a-1bcb-7823-b67e-505eb5b943f0_terseLabel_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:label id="lab_bsprt_ClassAUnitsMember_label_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class A Units [Member]</link:label>
    <link:label id="lab_bsprt_ClassAUnitsMember_documentation_en-US" xlink:label="lab_bsprt_ClassAUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class A Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ClassAUnitsMember" xlink:href="bsprt-20260930.xsd#bsprt_ClassAUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ClassAUnitsMember" xlink:to="lab_bsprt_ClassAUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019ff14a-1c3b-706b-b979-c007a870058b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Spread</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019ff14a-1c3b-75ed-9dc8-f1347b597fd4_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Spread</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_019ff14a-1b49-7a56-bee9-0509e42bd960_terseLabel_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_label_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Movement in Mortgage Loans on Real Estate [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MovementInMortgageLoansOnRealEstateRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:to="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_019ff14a-1bcb-7a8e-9e10-0743969b8095_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019ff14a-1bcb-74d8-9460-1b19842c1308_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income/(Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity_019ff14a-1c3c-7fcb-acce-29c8c420ca05_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Contributed To Variable Interest Entity</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Contributed To Variable Interest Entity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansContributedToVariableInterestEntity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:to="lab_bsprt_CommercialMortgageLoansContributedToVariableInterestEntity" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust_019ff14a-1c3b-7aa0-9ed4-ca431bb7b38f_terseLabel_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation of CMBS trust</link:label>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust_label_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Consolidation of CMBS Trust</link:label>
    <link:label id="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust_documentation_en-US" xlink:label="lab_bsprt_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetConsolidationOfCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Consolidation of CMBS Trust</link:label>
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    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_019ff14a-1b48-7f66-b5d5-81c5e3adfde7_terseLabel_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing and ancillary fees</link:label>
    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_label_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ancillary Fee Income Generated by Servicing Financial Assets, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount"/>
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    <link:label id="lab_us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock_019ff14a-1bcb-716e-a8cf-90b611a55b0f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loss Contingencies by Contingency</link:label>
    <link:label id="lab_us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Loss Contingencies by Contingency [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfLossContingenciesByContingencyTextBlock"/>
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    <link:label id="lab_us-gaap_PaymentsOfDividends_019ff14a-1bcb-7ff5-95c7-4a023e4106fe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividends_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividends" xlink:to="lab_us-gaap_PaymentsOfDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019ff14a-1aa9-7fb7-9b71-ce64da8b6918_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_019ff14a-1b49-7405-9e9e-12db644ada56_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
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    <link:label id="lab_us-gaap_StatementLineItems_019ff14a-1b49-7ddf-8acb-6d2bd4ebdeb4_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019ff14a-1aa9-76b5-a7ee-379e3ced54a8_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019ff14a-1aa9-7844-bbcb-7c4157d263b6_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebtCurrent_019ff14a-1bcb-772b-a1d4-3833d3159816_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured notes</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebtCurrent_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnsecuredDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebtCurrent" xlink:to="lab_us-gaap_UnsecuredDebtCurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InternalCreditAssessmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentDomain" xlink:to="lab_us-gaap_InternalCreditAssessmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_019ff14a-1bcb-7342-87fb-08242a2f5670_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_019ff14a-1bcb-714e-824c-241e0a874b41_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell_019ff14a-1bcb-7b51-8c4d-cd080b111008_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded commitments to fund loans and sell loans</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Commitment to Purchase or Sell, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:to="lab_us-gaap_LoansAndLeasesReceivableCommitmentsToPurchaseOrSell" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale_019ff14a-1c3c-743a-a953-5ae6d32d2166_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of commercial mortgage loans, held for sale to consolidated VIE CMBS trust</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Transferred TO VIE CMBS Trust, Held-for-Sale</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Transferred TO VIE CMBS Trust, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:to="lab_bsprt_CommercialMortgageLoansTransferredTOVIECMBSTrustHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_019ff14a-1bcb-741a-9180-3c558f689668_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:to="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable_019ff14a-1bcb-727a-83b6-8d76d1674f96_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Assets Sold under Agreements to Repurchase [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Sold under Agreement to Repurchase [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:to="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019ff14a-1bcb-71ae-9585-1395ad1f18d8_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_019ff14a-1c3b-7e22-a69d-446a62b0f27f_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesRate_019ff14a-1b49-748d-afc2-2502600f3402_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annualized Effective Service Fee Rate</link:label>
    <link:label id="lab_us-gaap_ManagementAndServiceFeesRate_label_en-US" xlink:label="lab_us-gaap_ManagementAndServiceFeesRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management and Service Fees, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementAndServiceFeesRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementAndServiceFeesRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementAndServiceFeesRate" xlink:to="lab_us-gaap_ManagementAndServiceFeesRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FloatingRateMember_019ff14a-1b49-7d93-a41a-4d0d244733ab_terseLabel_en-US" xlink:label="lab_bsprt_FloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating Rate</link:label>
    <link:label id="lab_bsprt_FloatingRateMember_label_en-US" xlink:label="lab_bsprt_FloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Floating Rate [Member]</link:label>
    <link:label id="lab_bsprt_FloatingRateMember_documentation_en-US" xlink:label="lab_bsprt_FloatingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Floating Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FloatingRateMember" xlink:href="bsprt-20260930.xsd#bsprt_FloatingRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FloatingRateMember" xlink:to="lab_bsprt_FloatingRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_019ff14a-1aa9-7d82-8f88-014428dc4040_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022-FL8 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL8 [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2022-FL8</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:href="bsprt-20260930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2022FL8Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_019ff14a-1bcb-7705-bddf-082d6b3f2d83_terseLabel_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management and subordinated performance fee</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_019ff14a-1bcb-735a-99fd-af50dbee6e9d_verboseLabel_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Asset management and subordinated performance fee</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_label_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management And Subordinated Performance Fees</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees_documentation_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management And Subordinated Performance Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:href="bsprt-20260930.xsd#bsprt_AssetManagementAndSubordinatedPerformanceFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:to="lab_bsprt_AssetManagementAndSubordinatedPerformanceFees" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019ff14a-1aa9-7788-badb-459412e802c6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating2Member_019ff14a-1aa9-7f95-a617-c1d7648cc429_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2</link:label>
    <link:label id="lab_bsprt_InvestmentRating2Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 2 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating2Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating2Member" xlink:href="bsprt-20260930.xsd#bsprt_InvestmentRating2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating2Member" xlink:to="lab_bsprt_InvestmentRating2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019ff14a-1b48-7c2c-b900-fa45bffb564d_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_019ff14a-1b48-7284-bb7b-603fcd09cfbc_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_019ff14a-1b48-76c9-8797-304b6560abb3_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_01a164c7-5f0f-7143-9282-291c6a22f328_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Financial Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_DerivativeLiabilityNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019ff14a-1b49-7f23-8dc0-ae8bbffb63f3_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_019ff14a-1bcb-7759-a96e-c5d8a7dd5908_terseLabel_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS Bonds</link:label>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_label_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Collateralized Loan Obligations [Member]</link:label>
    <link:label id="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember_documentation_en-US" xlink:label="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Real Estate Collateralized Loan Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:href="bsprt-20260930.xsd#bsprt_CommercialRealEstateCollateralizedLoanObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:to="lab_bsprt_CommercialRealEstateCollateralizedLoanObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_019ff14a-1b48-7ce6-8302-08415cc94086_negatedLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Principal repayments</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Collections of Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MortgageLoansOnRealEstateCollectionsOfPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:to="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019ff14a-1aa9-7dd9-a815-d13e1044bdd1_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_019ff14a-1aa9-7041-add5-6925a234a630_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019ff14a-1bcb-7438-b9d8-cc55324af290_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolver Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ASAPWHLineOfCreditMember_019ff14a-1b49-7da8-82d1-0a2887c58cb4_terseLabel_en-US" xlink:label="lab_bsprt_ASAPWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASAP WH Line of Credit</link:label>
    <link:label id="lab_bsprt_ASAPWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_ASAPWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ASAP WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_ASAPWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_ASAPWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">ASAP WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ASAPWHLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_ASAPWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ASAPWHLineOfCreditMember" xlink:to="lab_bsprt_ASAPWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019ff14a-1bcb-7326-8d03-059fe3b70c4c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ff14a-1bcb-7d3e-a43f-36c0f0a9a552_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ff14a-1bcb-708f-ac85-6dab14bc035e_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ff14a-1bcb-7e0a-8d1a-3a37be4246e9_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019ff14a-1bcb-70e7-b13d-2c4382c4d651_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Not Carried at Fair Value</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract_019ff14a-1b49-76fa-ab63-402d5c18dc72_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Securities Sold under Agreements to Repurchase [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:to="lab_us-gaap_OffsettingSecuritiesSoldUnderAgreementsToResellAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_019ff14a-1bcb-7548-9375-d61407084501_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentPastDueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019ff14a-1bcb-761c-aace-1f102bdb07f0_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FannieMaeMember_019ff14a-1b49-7499-bcad-e9ab2b093ca9_terseLabel_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:label id="lab_bsprt_FannieMaeMember_label_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fannie Mae [Member]</link:label>
    <link:label id="lab_bsprt_FannieMaeMember_documentation_en-US" xlink:label="lab_bsprt_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FannieMaeMember" xlink:href="bsprt-20260930.xsd#bsprt_FannieMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FannieMaeMember" xlink:to="lab_bsprt_FannieMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_019ff14a-1bcb-7f20-b17c-d0184b3bb92f_terseLabel_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period of loans held-for-sale sold</link:label>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_label_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Period of Loans Held-for-Sale Sold</link:label>
    <link:label id="lab_bsprt_PeriodOfLoansHeldForSaleSold_documentation_en-US" xlink:label="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Period of Loans Held-for-Sale Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PeriodOfLoansHeldForSaleSold" xlink:href="bsprt-20260930.xsd#bsprt_PeriodOfLoansHeldForSaleSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PeriodOfLoansHeldForSaleSold" xlink:to="lab_bsprt_PeriodOfLoansHeldForSaleSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_019ff14a-1b48-7331-826a-6e7a3a2a8dfd_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InternalCreditAssessmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InternalCreditAssessmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InternalCreditAssessmentAxis" xlink:to="lab_us-gaap_InternalCreditAssessmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019ff14a-1aa9-782b-90c1-a72004538826_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherUSStatesMember_019ff14a-1aa8-78f2-af01-43ee06551f31_terseLabel_en-US" xlink:label="lab_bsprt_OtherUSStatesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_bsprt_OtherUSStatesMember_label_en-US" xlink:label="lab_bsprt_OtherUSStatesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other US States [Member]</link:label>
    <link:label id="lab_bsprt_OtherUSStatesMember_documentation_en-US" xlink:label="lab_bsprt_OtherUSStatesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other US States</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherUSStatesMember" xlink:href="bsprt-20260930.xsd#bsprt_OtherUSStatesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherUSStatesMember" xlink:to="lab_bsprt_OtherUSStatesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019ff14a-1c3b-7387-ab50-603a69b448a8_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain/(Loss) from Investments</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_019ff14a-1c3b-79e1-8329-70a1d8ee7202_verboseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain/(loss)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:to="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_019ff14a-1bcb-7572-bdeb-3c251ddb413f_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019ff14a-1b49-7492-a204-1744e01a7681_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_019ff14a-1b48-7e72-9a27-b30a30f74542_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year four, originated in prior fiscal year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions_019ff14a-1bcb-7f0c-8a40-fe7f85d255f4_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtAmortizedValueAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:to="lab_us-gaap_ServicingAssetAtAmortizedValueAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_019ff14a-1c3b-7182-b51b-e2a15f3cde84_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Assets</link:label>
    <link:label id="lab_us-gaap_OffsettingAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAssetsTableTextBlock" xlink:to="lab_us-gaap_OffsettingAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_019ff14a-1b49-7f4d-859f-a9369cca6a7c_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets acquired</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_019ff14a-1bcb-7bd0-aee4-2b5bd77f5d29_terseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BSPRT2023FL10IssuerLtd.Member_01a164e4-73d3-7e65-87a3-53675212bcf0_terseLabel_en-US" xlink:label="lab_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BSPRT 2023-FL10 Issuer, Ltd.</link:label>
    <link:label id="lab_bsprt_BSPRT2023FL10IssuerLtd.Member_label_en-US" xlink:label="lab_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BSPRT 2023-FL10 Issuer, Ltd. [Member]</link:label>
    <link:label id="lab_bsprt_BSPRT2023FL10IssuerLtd.Member_documentation_en-US" xlink:label="lab_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BSPRT 2023-FL10 Issuer, Ltd.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:href="bsprt-20260930.xsd#bsprt_BSPRT2023FL10IssuerLtd.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:to="lab_bsprt_BSPRT2023FL10IssuerLtd.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019ff14a-1bcb-7745-a442-1cad7f341bea_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total Revenue/Investment Income</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019ff14a-1bcb-7d37-8289-4cf9f9ac39e6_netLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Referral fee income</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_019ff14a-1bcb-7cdc-b5ba-47f94722326b_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer to held for sale</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer To Held For Sale</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer To Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateTransferToHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:to="lab_bsprt_MortgageLoansOnRealEstateTransferToHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_019ff14a-1aa9-7fbb-ad07-ced67b0b6876_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on repurchase agreements and revolving credit facilities - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_label_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:label id="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from Securities Purchased under Agreements to Resell, Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:href="bsprt-20260930.xsd#bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:to="lab_bsprt_ProceedsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock_019ff14a-1b49-7372-a2bf-c9d2c67d6e59_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Liabilities at Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Liabilities at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_019ff14a-1c3b-7ee7-891a-64dc25b3821f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ZeldaPGJVHoldCoLLCMember_019ff14a-1b49-7e99-bd57-3cb313620653_terseLabel_en-US" xlink:label="lab_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Zelda PG JV HoldCo LLC</link:label>
    <link:label id="lab_bsprt_ZeldaPGJVHoldCoLLCMember_label_en-US" xlink:label="lab_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Zelda PG JV HoldCo LLC [Member]</link:label>
    <link:label id="lab_bsprt_ZeldaPGJVHoldCoLLCMember_documentation_en-US" xlink:label="lab_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Zelda PG JV HoldCo LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_ZeldaPGJVHoldCoLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:to="lab_bsprt_ZeldaPGJVHoldCoLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_019ff14a-1b49-7a51-b30b-498b5137534a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchases</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_019ff14a-1b49-7711-99a5-788bec174fba_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock shares repurchased</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee_019ff14a-1c3b-7283-a8fd-d50c4b71fd4b_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of excess total return</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:href="bsprt-20260930.xsd#bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:to="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFee" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_019ff14a-1b49-7b7b-b1a9-5bcd347dfcfa_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsGrossExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsGrossExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_019ff14a-1bcb-7d47-aa1b-7ac200715004_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Owned, Held For Sale</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Sale [Table Text Block]</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedHeldForSaleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:to="lab_bsprt_RealEstateOwnedHeldForSaleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_019ff14a-1bcb-770e-bce8-3f36990b1f12_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestPayableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest Payable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInterestPayableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInInterestPayableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_019ff14a-1bcb-7acb-8973-87a26b300f88_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Sales/paydowns</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_019ff14a-1c3c-7fd8-bea7-81af16cf69a9_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment_01a157d6-c5ef-71c8-8f0c-e5ce48e07541_terseLabel_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property transferred from real estate owned, held for sale to real estate owned, held for investment</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment_label_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Investment</link:label>
    <link:label id="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment_documentation_en-US" xlink:label="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property Transferred From Real Estate Owned, Held-for-Investment To Real Estate Owned, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:href="bsprt-20260930.xsd#bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:to="lab_bsprt_PropertyTransferredFromRealEstateOwnedHeldForInvestmentToRealEstateOwnedHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_019ff14a-1b49-7624-ae29-fc1d930132dc_terseLabel_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_label_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Amortization Expense, after Year Four</link:label>
    <link:label id="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Amortization Expense, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:href="bsprt-20260930.xsd#bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:to="lab_bsprt_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_019ff14a-1b49-70ac-862b-95ce72577d11_terseLabel_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted Numerator</link:label>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_label_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diluted Numerator [Abstract]</link:label>
    <link:label id="lab_bsprt_DilutedNumeratorAbstract_documentation_en-US" xlink:label="lab_bsprt_DilutedNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diluted Numerator</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DilutedNumeratorAbstract" xlink:href="bsprt-20260930.xsd#bsprt_DilutedNumeratorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DilutedNumeratorAbstract" xlink:to="lab_bsprt_DilutedNumeratorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GSRepoFacilityMember_01a03784-d464-74e3-b69f-6070742ef853_terseLabel_en-US" xlink:label="lab_bsprt_GSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GS Repo Facility</link:label>
    <link:label id="lab_bsprt_GSRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_GSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GS Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_GSRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_GSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GS Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GSRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_GSRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GSRepoFacilityMember" xlink:to="lab_bsprt_GSRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_June2025MultifamilyMember_01a15304-4257-7960-8c81-376320084403_terseLabel_en-US" xlink:label="lab_bsprt_June2025MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">June 2025 Multifamily</link:label>
    <link:label id="lab_bsprt_June2025MultifamilyMember_label_en-US" xlink:label="lab_bsprt_June2025MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">June 2025 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_June2025MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_June2025MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">June 2025 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_June2025MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_June2025MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_June2025MultifamilyMember" xlink:to="lab_bsprt_June2025MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019ff14a-1bcb-7c62-b382-91dadf07c33e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EscrowDeposit_019ff14a-1c3c-79ad-8ea4-13ad427033b8_terseLabel_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Escrow deposit</link:label>
    <link:label id="lab_us-gaap_EscrowDeposit_label_en-US" xlink:label="lab_us-gaap_EscrowDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Escrow Deposit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EscrowDeposit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EscrowDeposit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EscrowDeposit" xlink:to="lab_us-gaap_EscrowDeposit" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_019ff14a-1aa9-727f-8cf9-22d9be976424_terseLabel_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average risk rating of loans</link:label>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_label_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Risk Rating Of Loans</link:label>
    <link:label id="lab_bsprt_WeightedAverageRiskRatingOfLoans_documentation_en-US" xlink:label="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Risk Rating of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WeightedAverageRiskRatingOfLoans" xlink:href="bsprt-20260930.xsd#bsprt_WeightedAverageRiskRatingOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WeightedAverageRiskRatingOfLoans" xlink:to="lab_bsprt_WeightedAverageRiskRatingOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SouthwestMember_019ff14a-1b48-717d-ac9c-7d4ea651eba4_terseLabel_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Southwest</link:label>
    <link:label id="lab_bsprt_SouthwestMember_label_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Southwest [Member]</link:label>
    <link:label id="lab_bsprt_SouthwestMember_documentation_en-US" xlink:label="lab_bsprt_SouthwestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Southwest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SouthwestMember" xlink:href="bsprt-20260930.xsd#bsprt_SouthwestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SouthwestMember" xlink:to="lab_bsprt_SouthwestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MultifamilyMember_019ff14a-1aa9-7e32-90fc-2a9d9101056f_terseLabel_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multifamily</link:label>
    <link:label id="lab_srt_MultifamilyMember_label_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multifamily [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MultifamilyMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MultifamilyMember" xlink:to="lab_srt_MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_019ff14a-1bcb-7ee6-9ab8-3032ac866c22_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_019ff14a-1b48-7925-a700-6feb7d8fb4c1_terseLabel_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments [Roll Forward]</link:label>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_label_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments [Roll Forward]</link:label>
    <link:label id="lab_bsprt_NonPerformingFinancialInstrumentsRollForward_documentation_en-US" xlink:label="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Performing Financial Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:href="bsprt-20260930.xsd#bsprt_NonPerformingFinancialInstrumentsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:to="lab_bsprt_NonPerformingFinancialInstrumentsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_019ff14a-1bcb-71e6-b27d-b3c9754741df_terseLabel_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance acquired in acquisition</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_label_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Allowance Acquired in Acquisition</link:label>
    <link:label id="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition_documentation_en-US" xlink:label="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual Allowance Acquired in Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:href="bsprt-20260930.xsd#bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:to="lab_bsprt_LossContingencyAccrualAllowanceAcquiredInAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AccruedInterestReceivableNetCurrent_019ff14a-1bcb-7478-8619-1535a737b27e_terseLabel_en-US" xlink:label="lab_bsprt_AccruedInterestReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
    <link:label id="lab_bsprt_AccruedInterestReceivableNetCurrent_label_en-US" xlink:label="lab_bsprt_AccruedInterestReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Interest Receivable, Net, Current</link:label>
    <link:label id="lab_bsprt_AccruedInterestReceivableNetCurrent_documentation_en-US" xlink:label="lab_bsprt_AccruedInterestReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Interest Receivable, Net, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AccruedInterestReceivableNetCurrent" xlink:href="bsprt-20260930.xsd#bsprt_AccruedInterestReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AccruedInterestReceivableNetCurrent" xlink:to="lab_bsprt_AccruedInterestReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement_01a164c8-ddde-7ec3-98ff-99b5e8d01844_totalLabel_en-US" xlink:label="lab_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, Net Amount of Liabilities Presented on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_SecuritySoldUnderAgreementToRepurchaseAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019ff14a-1bcb-7613-8303-366106bf5f1e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019ff14a-1bcb-7ac4-921b-81555d2ba8a7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_019ff14a-1bcb-7aa5-ac99-5a3388264154_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
    <link:label id="lab_us-gaap_NotesPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableFairValueDisclosure" xlink:to="lab_us-gaap_NotesPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockOptionMember_019ff14a-1bcb-70e3-bf44-2e8e339e03bd_terseLabel_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_StockOptionMember_label_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockOptionMember" xlink:to="lab_us-gaap_StockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_019ff14a-1b49-7864-b38b-e61cced49dcd_terseLabel_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and beyond</link:label>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_label_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, After Year Four</link:label>
    <link:label id="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:href="bsprt-20260930.xsd#bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:to="lab_bsprt_LessorOperatingLeasePaymentToBeReceivedAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_AZ_019ff14a-1aa9-7cd3-aeaa-f3d8ebf3a680_terseLabel_en-US" xlink:label="lab_stpr_AZ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ARIZONA</link:label>
    <link:label id="lab_stpr_AZ_label_en-US" xlink:label="lab_stpr_AZ" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ARIZONA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_AZ" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_AZ"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_AZ" xlink:to="lab_stpr_AZ" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019ff14a-1aa9-761a-aa2b-c63c36970325_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_019ff14a-1bcb-7305-b72f-3a40f76c492d_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Allowance for Credit Losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019ff14a-1b49-7699-b9c6-f8451b520ec8_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VIEAssetsMeasuredAtFairValueMember_019ff14a-1c3c-7705-808f-e706a931a3d1_verboseLabel_en-US" xlink:label="lab_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">VIE assets, measured at fair value</link:label>
    <link:label id="lab_bsprt_VIEAssetsMeasuredAtFairValueMember_label_en-US" xlink:label="lab_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">VIE Assets, Measured At Fair Value [Member]</link:label>
    <link:label id="lab_bsprt_VIEAssetsMeasuredAtFairValueMember_documentation_en-US" xlink:label="lab_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">VIE Assets, Measured At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:href="bsprt-20260930.xsd#bsprt_VIEAssetsMeasuredAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:to="lab_bsprt_VIEAssetsMeasuredAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019ff14a-1bcb-7ea1-81db-a447ac193c0c_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019ff14a-1bcb-77a6-9784-14f24d997ccf_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FixedRateMember_019ff14a-1aa9-7c15-93fe-c93d27c83b01_terseLabel_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Rate</link:label>
    <link:label id="lab_bsprt_FixedRateMember_label_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate [Member]</link:label>
    <link:label id="lab_bsprt_FixedRateMember_documentation_en-US" xlink:label="lab_bsprt_FixedRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FixedRateMember" xlink:href="bsprt-20260930.xsd#bsprt_FixedRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FixedRateMember" xlink:to="lab_bsprt_FixedRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019ff14a-1c3c-775f-9d51-b48d3b2f38af_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_019ff14a-1bcb-7c6b-ae4d-5bae5f6bbd11_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Depreciation</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedDepreciation_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedDepreciation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedDepreciation" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedDepreciation" xlink:to="lab_bsprt_RealEstateOwnedDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019ff14a-1b48-7b91-940a-5beee223faf0_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_CA_019ff14a-1bcb-7ee0-8dbc-55ab8138d357_terseLabel_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">California</link:label>
    <link:label id="lab_stpr_CA_label_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CALIFORNIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_CA" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_CA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_CA" xlink:to="lab_stpr_CA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnitsOfPartnershipInterestAmount_01a164eb-d697-716a-99aa-7273a08fbe3e_terseLabel_en-US" xlink:label="lab_us-gaap_UnitsOfPartnershipInterestAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Units of partnership interest, amount (in shares)</link:label>
    <link:label id="lab_us-gaap_UnitsOfPartnershipInterestAmount_label_en-US" xlink:label="lab_us-gaap_UnitsOfPartnershipInterestAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Units of Partnership Interest, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnitsOfPartnershipInterestAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnitsOfPartnershipInterestAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnitsOfPartnershipInterestAmount" xlink:to="lab_us-gaap_UnitsOfPartnershipInterestAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_019ff14a-1b49-742c-8e47-d96264527742_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on other real estate investments</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gains (Losses) on Sales of Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnSalesOfOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:to="lab_us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_019ff14a-1bcb-760b-97d0-43761eea9d8a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Earnings (Loss) since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:to="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019ff14a-1bcb-7e6d-b6b9-6a0825ea6c48_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019ff14a-1bcb-747a-b04b-e62fc5dbfb27_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ExitCapitalizationRate_019ff14a-1bcb-7ebb-be01-d83723c4d12e_terseLabel_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit capitalization rate</link:label>
    <link:label id="lab_bsprt_ExitCapitalizationRate_label_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exit Capitalization Rate</link:label>
    <link:label id="lab_bsprt_ExitCapitalizationRate_documentation_en-US" xlink:label="lab_bsprt_ExitCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exit Capitalization Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ExitCapitalizationRate" xlink:href="bsprt-20260930.xsd#bsprt_ExitCapitalizationRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ExitCapitalizationRate" xlink:to="lab_bsprt_ExitCapitalizationRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_019ff14a-1b48-7a8b-af39-482929ed92e0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019ff14a-1b49-777b-99f9-1c198579abb0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_019ff14a-1c3b-724d-bae9-e421f120f0e6_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_019ff14a-1b48-7784-981b-fed89d8d4c7b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_019ff14a-1bcb-7240-a1fd-f4832ea103c6_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLenderDomain_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Lender [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityLenderDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLenderDomain" xlink:to="lab_us-gaap_LineOfCreditFacilityLenderDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease_019ff14a-1bcb-7fd4-bbb8-ea7a0d31144c_terseLabel_en-US" xlink:label="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions/(distributions) in non-controlling interest, net</link:label>
    <link:label id="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease_label_en-US" xlink:label="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Net Increase (Decrease)</link:label>
    <link:label id="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease_documentation_en-US" xlink:label="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Net Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:href="bsprt-20260930.xsd#bsprt_NoncontrollingInterestNetIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:to="lab_bsprt_NoncontrollingInterestNetIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_019ff14a-1b48-7446-807d-952f14004ef6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGoodwillTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTable" xlink:to="lab_us-gaap_ScheduleOfGoodwillTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_019ff14a-1b49-7738-9b6c-4f4b142b5f5c_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining amount available under share repurchase program</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Remaining Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash_019ff14a-1b49-7492-983d-79daeb94c697_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts not offset on the balance sheet, Cash Collateral</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RetailSiteMember_019ff14a-1b49-75e4-9bc6-f4bc230d941a_terseLabel_en-US" xlink:label="lab_srt_RetailSiteMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retail</link:label>
    <link:label id="lab_srt_RetailSiteMember_label_en-US" xlink:label="lab_srt_RetailSiteMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retail Site [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RetailSiteMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RetailSiteMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RetailSiteMember" xlink:to="lab_srt_RetailSiteMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019ff14a-1b48-7f78-bb43-0ef8c2c249ae_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019ff14a-1bcb-7336-acf8-9ce3de068065_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems_019ff14a-1c3b-752a-a922-79b0d132b5bb_terseLabel_en-US" xlink:label="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compliance with Regulatory Capital Requirements for Mortgage Companies [Line Items]</link:label>
    <link:label id="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems_label_en-US" xlink:label="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compliance with Regulatory Capital Requirements for Mortgage Companies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems" xlink:to="lab_us-gaap_ComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_019ff14a-1b48-7ab4-a9ed-488186ca5160_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-lived intangible, carrying value</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019ff14a-1aa9-7cc4-8dc7-ad4979c206af_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019ff14a-1c3b-76ae-90af-fe106858ce5b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) from equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019ff14a-1c3b-73c0-97ad-23264d8efb29_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income/(loss) from equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_019ff14a-1b49-7ab3-9d27-c40d4046ac8e_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember_019ff14a-1bcb-79cf-89f9-233bdc9cce5b_terseLabel_en-US" xlink:label="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Shares and Restricted Stock Units</link:label>
    <link:label id="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember_label_en-US" xlink:label="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock and Restricted Stock Units [Member]</link:label>
    <link:label id="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock and Restricted Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:href="bsprt-20260930.xsd#bsprt_RestrictedStockAndRestrictedStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:to="lab_bsprt_RestrictedStockAndRestrictedStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentNumberOfExtensionOptions_019ff14a-1b49-7405-85c2-2b5c4c873277_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of extension options</link:label>
    <link:label id="lab_bsprt_DebtInstrumentNumberOfExtensionOptions_label_en-US" xlink:label="lab_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Number Of Extension Options</link:label>
    <link:label id="lab_bsprt_DebtInstrumentNumberOfExtensionOptions_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Number of Extension Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:href="bsprt-20260930.xsd#bsprt_DebtInstrumentNumberOfExtensionOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:to="lab_bsprt_DebtInstrumentNumberOfExtensionOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_019ff14a-1aa9-7bcf-af8b-0ebfafd0f28b_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019ff14a-1bcb-7e1a-9d17-feceef5f7ed0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019ff14a-1b48-7746-b1d9-7a3cde5b337d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ForeclosedPropertyConstructionInProgressMember_019ff14a-1c3c-71ea-89e3-dcd80c69eea2_terseLabel_en-US" xlink:label="lab_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreclosed Property Construction In Progress</link:label>
    <link:label id="lab_bsprt_ForeclosedPropertyConstructionInProgressMember_label_en-US" xlink:label="lab_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreclosed Property Construction In Progress [Member]</link:label>
    <link:label id="lab_bsprt_ForeclosedPropertyConstructionInProgressMember_documentation_en-US" xlink:label="lab_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Foreclosed Property Construction In Progress</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:href="bsprt-20260930.xsd#bsprt_ForeclosedPropertyConstructionInProgressMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:to="lab_bsprt_ForeclosedPropertyConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019ff14a-1b48-7693-bf14-d306f84b4166_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (October-December)</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019ff14a-1b48-7d44-816b-6a1e9457c0ab_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019ff14a-1b48-72e9-a086-de5de44686f4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level III</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_019ff14a-1b48-7085-a283-3aadee1a1e6d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral</link:label>
    <link:label id="lab_us-gaap_AssetPledgedAsCollateralMember_label_en-US" xlink:label="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Pledged as Collateral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetPledgedAsCollateralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetPledgedAsCollateralMember" xlink:to="lab_us-gaap_AssetPledgedAsCollateralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_019ff14a-1b48-7ce9-a86f-41b21f94ae0d_verboseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockSharesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockSharesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockSharesAcquired" xlink:to="lab_us-gaap_TreasuryStockSharesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019ff14a-1bcb-74e6-a3d2-0d4713d042c1_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_01a1668d-235a-79b0-8bf8-88eaf2773152_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ownership percentage</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019ff14a-1c3b-7dea-aadc-672b9749dcc7_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest, ownership percentage by noncontrolling owners</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_019ff14a-1bcb-7d0f-83ee-85eb2e8e7348_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCash_019ff14a-1b48-75fa-bea0-8d1984578dd8_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">CLO cash held by servicer</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_019ff14a-1b48-7be0-be07-4654a4bd7a34_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCash" xlink:to="lab_us-gaap_RestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_019ff14a-1b49-71e1-b261-d65229f8738e_totalLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total future minimum rent</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_019ff14a-1c3b-73c9-982a-c9c8499cc564_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_label_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Commercial Mortgage Loans Held-For-Investment</link:label>
    <link:label id="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Commercial Mortgage Loans Held-For-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:href="bsprt-20260930.xsd#bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:to="lab_bsprt_ProceedsFromSaleOfCommercialMortgageLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageLoansHeldForSaleMember_019ff14a-1bcb-7824-93e6-18bb590845dc_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Held For Sale</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansHeldForSaleMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Held For Sale [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageLoansHeldForSaleMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageLoansHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:to="lab_bsprt_CommercialMortgageLoansHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019ff14a-1c3c-7198-a5bc-1d0f41f9ec98_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities_019ff14a-1b48-7a22-9d78-ed9113c43b5b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale/(purchase) of derivative instruments</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Derivative Instrument, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromDerivativeInstrumentInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR_019ff14a-1bcb-7498-99c5-5fd6dfb410fb_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired MSRs at July 1, 2025</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Mortgage Servicing Rights (MSR)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireMortgageServicingRightsMSR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:to="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_019ff14a-1bcb-78ef-b3c2-05065dc3a819_negatedLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Transfer to real estate owned</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Transfer On Foreclosure</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Transfer on Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateTransferOnForeclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:to="lab_bsprt_MortgageLoansOnRealEstateTransferOnForeclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_019ff14a-1b48-78b5-b5e9-8414463ba3df_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchases paid</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockValueAcquiredCostMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:to="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ff14a-1bcb-7d96-986f-d7fc07421b12_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ff14a-1bcb-793c-9f34-20b9c78f100c_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ff14a-1bcb-7dac-b1f2-505fc9b28e97_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash,</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_01a164c7-8853-7347-a4ba-77887450bd8c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Cash Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralRightToReclaimCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Collateral, Right to Reclaim Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:to="lab_us-gaap_DerivativeCollateralRightToReclaimCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019ff14a-1bcb-71f3-afaa-83cb2c52021a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_019ff14a-1bcb-7daa-837d-2da44849f287_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for Credit Losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:to="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019ff14a-1bcb-7dce-a8cf-1cb11fa0c679_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NewPointJVLLCMember_019ff14a-1bcb-76d4-8fd0-bdf50ffabe98_terseLabel_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC</link:label>
    <link:label id="lab_bsprt_NewPointJVLLCMember_label_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC [Member]</link:label>
    <link:label id="lab_bsprt_NewPointJVLLCMember_documentation_en-US" xlink:label="lab_bsprt_NewPointJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NewPoint JV LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NewPointJVLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_NewPointJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NewPointJVLLCMember" xlink:to="lab_bsprt_NewPointJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019ff14a-1c3b-71d1-90d2-437b023ee90c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019ff14a-1c3b-784b-9d31-d9f712cf4e34_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase of NewPoint Holdings JV LLC</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019ff14a-1bcb-732a-a137-2755c609a8a4_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_019ff14a-1bcb-7ef8-9a3e-54cf89fb15b0_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accrued Compensation</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accrued Compensation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAccruedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_019ff14a-1aa8-7f4e-b7fb-8b1a6afac811_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019ff14a-1b49-7289-8508-8f015e742067_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_GA_019ff14a-1b49-7497-a04d-13eb564adc90_terseLabel_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GEORGIA</link:label>
    <link:label id="lab_stpr_GA_label_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GEORGIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_GA" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_GA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_GA" xlink:to="lab_stpr_GA" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_019ff14a-1b49-7039-8a9d-26194b4c8b09_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019ff14a-1b48-70c5-99e3-ef618379a794_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019ff14a-1aa9-7f22-a7a3-a83625b42ebd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments for common stock repurchases</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019ff14a-1bcb-7857-926e-f629bdc73a50_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_019ff14a-1bcb-72bf-bd81-9ea0fb0931ed_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments, Gain (Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019ff14a-1b49-7d36-b811-795b0413105e_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_019ff14a-1b49-7714-b8e1-bf1512e4c72d_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (October-December)</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019ff14a-1bcb-7e09-a5de-bcf6a1876412_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions_019ff14a-1bcb-7660-85cb-e41dec7e6a4f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deferred fees and other items</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Other Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageLoansOnRealEstateOtherAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateOtherAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_FL_019ff14a-1bcb-7b45-a6d0-5d0718c3b4a9_terseLabel_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Florida</link:label>
    <link:label id="lab_stpr_FL_label_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">FLORIDA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_FL" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_FL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_FL" xlink:to="lab_stpr_FL" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019ff14a-1bcb-797a-9424-a3b126716cce_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_019ff14a-1bcb-7bde-9e30-0f8c038dec27_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019ff14a-1b48-7895-9ab5-b40e77a5a436_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_019ff14a-1bcb-74be-9138-32f534eb0676_terseLabel_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest on escrows</link:label>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_label_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Earned on Escrows</link:label>
    <link:label id="lab_bsprt_InterestEarnedOnEscrows_documentation_en-US" xlink:label="lab_bsprt_InterestEarnedOnEscrows" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Earned on Escrows</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InterestEarnedOnEscrows" xlink:href="bsprt-20260930.xsd#bsprt_InterestEarnedOnEscrows"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InterestEarnedOnEscrows" xlink:to="lab_bsprt_InterestEarnedOnEscrows" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_019ff14a-1aa9-7501-baa3-493a0d01bad2_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_019ff14a-1aa9-7ce4-9985-38f56e2d55a0_terseLabel_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JPM Repo Facility</link:label>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">JPM Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_JPMRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_JPMRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">JPM Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JPMRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_JPMRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JPMRepoFacilityMember" xlink:to="lab_bsprt_JPMRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_019ff14a-1bcb-744c-b259-193b16807d34_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee or Group of Investees</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee or Group of Investees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeOrGroupOfInvesteesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019ff14a-1aa9-78a5-9a53-5a29d9a78242_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary_019ff14a-1b48-70f9-90a8-e7df5fd836d9_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnFirstAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentAggregateCost_019ff14a-1aa9-7682-904c-a760f7b6b6ca_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Aggregate Cost</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentAggregateCost_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Aggregate Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentAggregateCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentAggregateCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentAggregateCost" xlink:to="lab_us-gaap_EquityMethodInvestmentAggregateCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019ff14a-1bcb-7fcd-8f88-5cadcdcd213c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_CO_019ff14a-1bcb-70d7-b765-4852d20f034a_terseLabel_en-US" xlink:label="lab_stpr_CO" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denver, CO</link:label>
    <link:label id="lab_stpr_CO_label_en-US" xlink:label="lab_stpr_CO" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">COLORADO</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_CO" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_CO"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_CO" xlink:to="lab_stpr_CO" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations_019ff14a-1bcb-7a93-8268-5d5e9dbfa848_terseLabel_en-US" xlink:label="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss sharing obligations</link:label>
    <link:label id="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations_label_en-US" xlink:label="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantee Obligations Included In Allowance For Loss Sharing Obligations</link:label>
    <link:label id="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations_documentation_en-US" xlink:label="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Guarantee Obligations Included In Allowance For Loss Sharing Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:href="bsprt-20260930.xsd#bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:to="lab_bsprt_GuaranteeObligationsIncludedInAllowanceForLossSharingObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_019ff14a-1bcb-722e-aa28-25abdb0a78f5_terseLabel_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value, discount rate, percentage</link:label>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_label_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Present Value, Discount Rate, Percentage</link:label>
    <link:label id="lab_bsprt_PresentValueDiscountRatePercentage_documentation_en-US" xlink:label="lab_bsprt_PresentValueDiscountRatePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Present Value, Discount Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PresentValueDiscountRatePercentage" xlink:href="bsprt-20260930.xsd#bsprt_PresentValueDiscountRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PresentValueDiscountRatePercentage" xlink:to="lab_bsprt_PresentValueDiscountRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstatePropertiesAxis_019ff14a-1c3c-73d9-bc7e-509ba86a38ee_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Property Ownership [Axis]</link:label>
    <link:label id="lab_us-gaap_RealEstatePropertiesAxis_label_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Property Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstatePropertiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstatePropertiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstatePropertiesAxis" xlink:to="lab_us-gaap_RealEstatePropertiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_019ff14a-1bcb-7fc4-b1a6-aada61951bd0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on real estate securities, available for sale</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019ff14a-1bcb-7f60-b54f-bbd80f3c99d8_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, redeemable convertible preferred stock and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_019ff14a-1bcb-79a5-aab8-f424a8b6c0a3_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease cost</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_019ff14a-1bcb-7ba7-95bf-d7f18ee36339_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originations</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_019ff14a-1aa9-7ca2-9908-94acfebdb89c_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019ff14a-1bcb-75b6-bf13-8f90ab57116a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_019ff14a-1aa9-73ee-bbbc-a687d2e3e6d3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019ff14a-1c3c-776a-ae8a-e3af055718a0_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019ff14a-1bcb-73f9-9191-c9d97f9de235_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019ff14a-1bcb-7f6f-911a-d84a9e954037_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_019ff14a-1b49-736b-8cf9-8490fb838526_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026 (October-December)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_019ff14a-1b49-7b15-8974-c12f65aac247_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (October - December)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019ff14a-1aa9-7246-89ae-c9020bffb196_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_019ff14a-1c3b-7cd0-9cc3-6fd54148cc59_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable Portfolio Segment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablePortfolioSegmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:to="lab_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_01a15d35-e642-7079-a78b-582ac178e743_terseLabel_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans transferred from commercial mortgage loans, held for investment to real estate owned, held for investment</link:label>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferToOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransferToOtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferToOtherRealEstate" xlink:to="lab_us-gaap_TransferToOtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_019ff14a-1bcb-7da3-8bd4-102fb3a32ccc_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_019ff14a-1bcb-7881-87ec-4e892a9cff2b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Preferred stock dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends and Other Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendsAndOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:to="lab_us-gaap_PreferredStockDividendsAndOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_019ff14a-1bcb-7e17-8d34-5c38e91de7c7_terseLabel_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fees per the fee arrangement</link:label>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_label_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fees Per The Fee Arrangement</link:label>
    <link:label id="lab_bsprt_FeesPerTheFeeArrangement_documentation_en-US" xlink:label="lab_bsprt_FeesPerTheFeeArrangement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fees Per The Fee Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FeesPerTheFeeArrangement" xlink:href="bsprt-20260930.xsd#bsprt_FeesPerTheFeeArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FeesPerTheFeeArrangement" xlink:to="lab_bsprt_FeesPerTheFeeArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_019ff14a-1b48-796f-81f0-a3eb567650b5_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, $0.01 par value; 100,000,000 shares authorized, 7.5% Cumulative Redeemable Preferred Stock, Series E, 10,329,039 shares issued and outstanding as of September&#160;30, 2026 and December&#160;31, 2025</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_019ff14a-1b48-75bd-9841-1cf6d32593f5_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Perpetual preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio_019ff14a-1bcb-7acb-98d6-d8150bd3ed1b_terseLabel_en-US" xlink:label="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UPB</link:label>
    <link:label id="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio_label_en-US" xlink:label="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-in-Portfolio, Principal Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:to="lab_us-gaap_PrincipalAmountOutstandingOfLoansHeldInPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_019ff14a-1bcb-77d4-86b2-a414b02b095a_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General allowance for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_019ff14a-1bcb-7b22-9e0d-3cb09e260dc5_netLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">General (provision)/benefit for credit losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_019ff14a-1bcb-76d8-84da-ec58e8df4c51_verboseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">General Allowance for Credit Losses</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_label_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, General [Member]</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossGeneralMember_documentation_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, General</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForCreditLossGeneralMember" xlink:href="bsprt-20260930.xsd#bsprt_AllowanceForCreditLossGeneralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForCreditLossGeneralMember" xlink:to="lab_bsprt_AllowanceForCreditLossGeneralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue_019ff14a-1aa9-7594-83cc-9e8227740323_terseLabel_en-US" xlink:label="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan commitments and forward sale commitments, net</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue_label_en-US" xlink:label="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Commitments And Forward Sale Commitments, Fair Value</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue_documentation_en-US" xlink:label="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Commitments And Forward Sale Commitments, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:href="bsprt-20260930.xsd#bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:to="lab_bsprt_LoanCommitmentsAndForwardSaleCommitmentsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_019ff14a-1bcb-786e-b3b5-af43df8add0e_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification adjustment for amounts included in net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_019ff14a-1bcb-7ab1-a7cb-94f7b489ddfa_terseLabel_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CreditConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CreditConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditConcentrationRiskMember" xlink:to="lab_us-gaap_CreditConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019ff14a-1bcb-7e8f-a28d-40a8c37f915c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash payments for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan_019ff14a-1aa8-7681-beed-d810329adaad_terseLabel_en-US" xlink:label="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock purchased through distribution reinvestment plan (in shares)</link:label>
    <link:label id="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan_label_en-US" xlink:label="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Purchased During Period, Shares, Dividend Reinvestment Plan</link:label>
    <link:label id="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan_documentation_en-US" xlink:label="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Purchased During Period, Shares, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:href="bsprt-20260930.xsd#bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:to="lab_bsprt_StockPurchasedDuringPeriodSharesDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_019ff14a-1b48-706d-a225-b2752d5ecc46_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Participating securities' share in earnings</link:label>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_label_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Participating Securities, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:to="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherGeneralExpense_019ff14a-1bcb-7e24-88a9-f9c7960a66b7_terseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expenses</link:label>
    <link:label id="lab_us-gaap_OtherGeneralExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherGeneralExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherGeneralExpense" xlink:to="lab_us-gaap_OtherGeneralExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019ff14a-1b49-795f-8d05-8c10d051cc2b_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019ff14a-1aa9-757f-af14-8f28b3539e3f_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets, at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019ff14a-1aa9-72ed-9893-6b8e5b0d82eb_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets, at fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_019ff14a-1c3b-78cb-bb03-c62a0f888b4a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:to="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember_019ff14a-1bcb-77f1-b755-88fce285acab_terseLabel_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition fees and expenses, including amount capitalized</link:label>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember_label_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition Fees And Expenses Including Amount Capitalized [Member]</link:label>
    <link:label id="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember_documentation_en-US" xlink:label="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Fees And Expenses Including Amount Capitalized [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:href="bsprt-20260930.xsd#bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:to="lab_bsprt_AcquisitionFeesAndExpensesIncludingAmountCapitalizedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019ff14a-1bcb-76b3-b097-bbed62595e5d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019ff14a-1b49-7e0c-80b5-76cd95015614_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_019ff14a-1b48-7038-aaba-fb7b4974b12a_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total redeemable convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_019ff14a-1b48-7589-83c9-88f783f710a2_verboseLabel_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_label_en-US" xlink:label="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Stock, Nonredeemable or Redeemable, Issuer Option, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:to="lab_us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019ff14a-1aa9-7960-b727-0a5bdc3b9e4a_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-In Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_019ff14a-1b49-7e8f-8fbb-fd6a7ce7a3b4_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_019ff14a-1bcb-7b57-9747-15c5df89fb4a_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgages Held For Sale Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgages Held For Sale Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgagesHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019ff14a-1b48-7800-b9fc-9c6e56d33f45_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_019ff14a-1b48-700c-9d49-3501fadf7da6_netLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ff14a-1bcb-7737-962f-b601efa15a21_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ff14a-1bcb-7b09-9e8c-d3ef253fa4f2_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ff14a-1bcb-7145-866f-a4524f93c414_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019ff14a-1bcb-7197-abe9-55e8e26db04b_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate_019ff14a-1c3c-75a2-a63e-73d913e86115_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate_label_en-US" xlink:label="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Assets and Servicing Liabilities at Fair Value, Assumptions Used to Estimate Fair Value, Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:to="lab_us-gaap_ServicingAssetsAndServicingLiabilitiesAtFairValueAssumptionsUsedToEstimateFairValueDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_019ff14a-1b49-7281-a9b4-df504864ec15_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR)</link:label>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_label_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredOvernightFinancingRateSofrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:to="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross_019ff14a-1aa9-7f56-86f4-57b2ef03d8d0_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, Gross Amounts of Recognized Liabilities</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseGross" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateDebtMember_019ff14a-1b48-776f-95c9-4412eadd6cd3_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Debt and Other Real Estate Investments</link:label>
    <link:label id="lab_bsprt_RealEstateDebtMember_label_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Debt [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateDebtMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateDebtMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateDebtMember" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateDebtMember" xlink:to="lab_bsprt_RealEstateDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_019ff14a-1b49-7523-acf4-8ce5d146355d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts and Financing Receivables [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAbstract_019ff14a-1aa9-7d7e-91c1-3727f03e24d1_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:label id="lab_us-gaap_RealEstateAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAbstract" xlink:to="lab_us-gaap_RealEstateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019ff14a-1bcb-7795-bc76-3734b7d4c9ca_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining lease term (in year)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SecuredDebtExcluded_019ff14a-1b48-7565-bdb3-ee147608cb7e_terseLabel_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligation excluded</link:label>
    <link:label id="lab_bsprt_SecuredDebtExcluded_label_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt Excluded</link:label>
    <link:label id="lab_bsprt_SecuredDebtExcluded_documentation_en-US" xlink:label="lab_bsprt_SecuredDebtExcluded" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secured Debt Excluded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SecuredDebtExcluded" xlink:href="bsprt-20260930.xsd#bsprt_SecuredDebtExcluded"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SecuredDebtExcluded" xlink:to="lab_bsprt_SecuredDebtExcluded" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_019ff14a-1bcb-7380-90e7-9d69fee6e33d_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility</link:label>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BarclaysRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_BarclaysRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BarclaysRepoFacilityMember" xlink:to="lab_bsprt_BarclaysRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_019ff14a-1aa9-7cb4-8996-5d6c4494990e_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanOriginationCommitmentsMember_019ff14a-1bcb-7d0d-ba04-f1f9a51d7613_terseLabel_en-US" xlink:label="lab_us-gaap_LoanOriginationCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded Commitments Under Commercial Mortgage Loans</link:label>
    <link:label id="lab_us-gaap_LoanOriginationCommitmentsMember_label_en-US" xlink:label="lab_us-gaap_LoanOriginationCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Origination Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanOriginationCommitmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoanOriginationCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanOriginationCommitmentsMember" xlink:to="lab_us-gaap_LoanOriginationCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019ff14a-1aa9-7f55-bf1d-7bbb24e2396d_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net change in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_019ff14a-1b48-7bff-b98b-7f9745b54e2c_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member_019ff14a-1b49-798b-8d3f-bf890cbc5586_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note III</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member_label_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note III, Maturing September 2036 [Member]</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note III, Maturing September 2036</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:href="bsprt-20260930.xsd#bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:to="lab_bsprt_JuniorSubordinatedNoteIIIMaturingSeptember2036Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation_019ff14a-1bcb-727e-b865-93189fd213d1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateOwnedAccumulatedDepreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:to="lab_us-gaap_RealEstateOwnedAccumulatedDepreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_019ff14a-1bcb-7ace-9baf-95fc85400ead_verboseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_019ff14a-1bcb-78a1-9136-fadf5a3031dc_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Revenue</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing of Financial Assets [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_019ff14a-1b49-73a9-b337-cc33f940cc6d_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance For Credit Losses</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Before Allowance For Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_019ff14a-1aa9-77db-9bed-155d5b662329_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedTwoYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ff14a-1aa9-787c-bbea-ed352b287102_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ff14a-1aa9-70e5-8f9b-7e50bfce5061_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019ff14a-1b49-7b07-b031-2d1f981e98bb_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OperatingPartnerMember_01a16141-1a86-790f-8d6e-000648009db6_terseLabel_en-US" xlink:label="lab_bsprt_OperatingPartnerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Partner</link:label>
    <link:label id="lab_bsprt_OperatingPartnerMember_label_en-US" xlink:label="lab_bsprt_OperatingPartnerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Partner [Member]</link:label>
    <link:label id="lab_bsprt_OperatingPartnerMember_documentation_en-US" xlink:label="lab_bsprt_OperatingPartnerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Partner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OperatingPartnerMember" xlink:href="bsprt-20260930.xsd#bsprt_OperatingPartnerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OperatingPartnerMember" xlink:to="lab_bsprt_OperatingPartnerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateAxis_01a16142-bad0-7736-a2e6-7d3c4be6f0f6_terseLabel_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate [Axis]</link:label>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateAxis_label_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate [Axis]</link:label>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateAxis_documentation_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProfitDistributionHurdleRateAxis" xlink:href="bsprt-20260930.xsd#bsprt_ProfitDistributionHurdleRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProfitDistributionHurdleRateAxis" xlink:to="lab_bsprt_ProfitDistributionHurdleRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_019ff14a-1b49-789d-814c-14b90904762d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019ff14a-1aa9-751b-be7c-a353c2df6fed_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Accumulated Other Comprehensive Income/(Loss)</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_019ff14a-1c3c-7776-9c02-78b4c3a97281_periodStartLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Amortized cost, beginning of period</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_019ff14a-1c3c-75c1-a74b-daded7f5b983_periodEndLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Amortized cost, end of period</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Commercial and Consumer, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateCommercialAndConsumerNet" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_019ff14a-1c3c-7726-9e04-aaf1c4db5d4d_terseLabel_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seller-based financing on sales of real estate owned, held for sale</link:label>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_label_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seller Based Financing On Sales Of Real Estate Owned Held For Sale</link:label>
    <link:label id="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale_documentation_en-US" xlink:label="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seller Based Financing On Sales Of Real Estate Owned Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:to="lab_bsprt_SellerBasedFinancingOnSalesOfRealEstateOwnedHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_019ff14a-1c3b-7480-aa13-4e750cd1e971_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization/accretion of fees and other items</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Accretion (Amortization) Of Discounts And Premiums</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Accretion (Amortization) of Discounts and Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:to="lab_bsprt_MortgageLoansOnRealEstateAccretionAmortizationOfDiscountsAndPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WFRepoFacilityMember_019ff14a-1b49-7ada-b3a5-8e3c2ebcee79_terseLabel_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">WF Repo Facility</link:label>
    <link:label id="lab_bsprt_WFRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">WF Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_WFRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_WFRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">WF Repo Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WFRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_WFRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WFRepoFacilityMember" xlink:to="lab_bsprt_WFRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_019ff14a-1c3b-743f-909d-81ae7c18e746_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasuryNotesSecuritiesMember_019ff14a-1bcb-77e2-9062-f73cc994c966_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury notes</link:label>
    <link:label id="lab_us-gaap_USTreasuryNotesSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Notes Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryNotesSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_USTreasuryNotesSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryNotesSecuritiesMember" xlink:to="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses_019ff14a-1bcb-76f0-b986-73a8dcbc1e71_terseLabel_en-US" xlink:label="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CECL reserves impact</link:label>
    <link:label id="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses_label_en-US" xlink:label="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impact Of Adopting Current Expected Credit Losses</link:label>
    <link:label id="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses_documentation_en-US" xlink:label="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impact Of Adopting Current Expected Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:href="bsprt-20260930.xsd#bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:to="lab_bsprt_ImpactOfAdoptingCurrentExpectedCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_May2022MultifamilyMember_01a15305-e680-798a-ba63-332e66990162_terseLabel_en-US" xlink:label="lab_bsprt_May2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">May 2022 Multifamily</link:label>
    <link:label id="lab_bsprt_May2022MultifamilyMember_label_en-US" xlink:label="lab_bsprt_May2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">May 2022 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_May2022MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_May2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">May 2022 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_May2022MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_May2022MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_May2022MultifamilyMember" xlink:to="lab_bsprt_May2022MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_019ff14a-1b48-72c3-b1ab-fac9ae06525b_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Avg. Life (in Years)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Remaining Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_019ff14a-1aa9-703c-a8b6-c0c0444b7c6d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset and Goodwill</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset and Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfIntangibleAssetsAndGoodwillTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NJ_019ff14a-1b49-7af3-8e2c-737b06382043_terseLabel_en-US" xlink:label="lab_stpr_NJ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Jersey</link:label>
    <link:label id="lab_stpr_NJ_label_en-US" xlink:label="lab_stpr_NJ" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW JERSEY</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NJ" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_NJ"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NJ" xlink:to="lab_stpr_NJ" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019ff14a-1b48-7941-9a72-dc062850ef23_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_019ff14a-1b48-7dac-9819-cde6857e6ee9_terseLabel_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit</link:label>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_JPMWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_JPMWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">JPM WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JPMWHLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_JPMWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JPMWHLineOfCreditMember" xlink:to="lab_bsprt_JPMWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019ff14a-1aa9-7365-9dec-b97ffce1927a_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NC_019ff14a-1bcb-7524-9c65-26c1c0cf0e2c_terseLabel_en-US" xlink:label="lab_stpr_NC" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NORTH CAROLINA</link:label>
    <link:label id="lab_stpr_NC_label_en-US" xlink:label="lab_stpr_NC" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NORTH CAROLINA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NC" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_NC"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NC" xlink:to="lab_stpr_NC" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_019ff14a-1b49-72f2-b25d-d2a5823a71a5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Gross Amounts Offset on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_019ff14a-1bcb-7529-8673-ac3ba54f0521_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition expenses</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition-Related Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AgencyLicenseIntangiblesMember_019ff14a-1bcb-7385-ad2f-bb53781d202a_terseLabel_en-US" xlink:label="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency License Intangibles</link:label>
    <link:label id="lab_bsprt_AgencyLicenseIntangiblesMember_label_en-US" xlink:label="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency License Intangibles [Member]</link:label>
    <link:label id="lab_bsprt_AgencyLicenseIntangiblesMember_documentation_en-US" xlink:label="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency License Intangibles</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AgencyLicenseIntangiblesMember" xlink:href="bsprt-20260930.xsd#bsprt_AgencyLicenseIntangiblesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AgencyLicenseIntangiblesMember" xlink:to="lab_bsprt_AgencyLicenseIntangiblesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019ff14a-1b49-79a9-96fd-ba793f8dc8fd_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.01 par value, 900,000,000 shares authorized, 75,881,209 and 81,553,982 shares issued and outstanding as of September&#160;30, 2026 and December&#160;31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_019ff14a-1b49-7cd3-bb0e-1a67b9c27dc0_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock value</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_019ff14a-1bcb-73bd-b9ca-ec2da0df466d_terseLabel_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average servicing fee (as basis points)</link:label>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_label_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Percentage</link:label>
    <link:label id="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage_documentation_en-US" xlink:label="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:href="bsprt-20260930.xsd#bsprt_ContractuallySpecifiedServicingFeesPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:to="lab_bsprt_ContractuallySpecifiedServicingFeesPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpense_019ff14a-1bcb-7864-9def-1814c8d57dd8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpense_label_en-US" xlink:label="lab_us-gaap_InterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating and Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpense" xlink:to="lab_us-gaap_InterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019ff14a-1b48-72e2-8f2d-e051f0d02fbf_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_019ff14a-1aa9-7803-a5fc-c2650be124bd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares cancelled for tax withholding on vested equity rewards</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_019ff14a-1bcb-7a44-9a6e-f0898f27f901_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Collateralized Loan Obligations by Tranche</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount_01a164e9-6ee1-7177-a670-485674b14680_terseLabel_en-US" xlink:label="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share repurchase program, increase (decrease) in authorized, amount</link:label>
    <link:label id="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount_label_en-US" xlink:label="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Increase (Decrease) In Authorized, Amount</link:label>
    <link:label id="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount_documentation_en-US" xlink:label="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Increase (Decrease) In Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:href="bsprt-20260930.xsd#bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:to="lab_bsprt_ShareRepurchaseProgramIncreaseDecreaseInAuthorizedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_019ff14a-1bcb-7a2c-8752-a53e7503e7c1_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_IndustrialPropertyMember_019ff14a-1b49-78f2-9eb0-55f6cc5e73be_terseLabel_en-US" xlink:label="lab_srt_IndustrialPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrial</link:label>
    <link:label id="lab_srt_IndustrialPropertyMember_label_en-US" xlink:label="lab_srt_IndustrialPropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrial Property [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_IndustrialPropertyMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_IndustrialPropertyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_IndustrialPropertyMember" xlink:to="lab_srt_IndustrialPropertyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_019ff14a-1bcb-7213-aea5-ae5822339779_terseLabel_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 90 days past due</link:label>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_label_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Less Than 90 Days Past Due [Member]</link:label>
    <link:label id="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember_documentation_en-US" xlink:label="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Asset, Less Than 90 Days Past Due</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:href="bsprt-20260930.xsd#bsprt_FinancialAssetLessThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:to="lab_bsprt_FinancialAssetLessThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract_019ff14a-1c3c-73bc-abb6-a43912599e7b_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite lived intangibles:</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, Indefinite-Lived [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwillAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019ff14a-1c3b-7860-a1d2-ba31830245c7_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillLineItems_019ff14a-1bcb-7ead-a484-68931c58fc8f_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditDefaultSwapMember_019ff14a-1b49-7117-bee9-b6c3ffdf3112_terseLabel_en-US" xlink:label="lab_us-gaap_CreditDefaultSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_CreditDefaultSwapMember_label_en-US" xlink:label="lab_us-gaap_CreditDefaultSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Default Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditDefaultSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditDefaultSwapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditDefaultSwapMember" xlink:to="lab_us-gaap_CreditDefaultSwapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_019ff14a-1b48-746d-a528-cf51be3cacb7_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions and originations</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, New Mortgage Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageLoansOnRealEstateNewMortgageLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_019ff14a-1bcb-77de-8f50-986ddf28608b_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan repurchase option liability</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Loan Repurchase Option Liability</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Loan Repurchase Option Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedLoanRepurchaseOptionLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NY_019ff14a-1b48-7879-9aa5-137917a2e761_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York</link:label>
    <link:label id="lab_stpr_NY_label_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW YORK</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NY" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_NY"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_NY" xlink:to="lab_stpr_NY" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaid_01a164e2-9921-7b5d-bac0-c77d734f2324_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid</link:label>
    <link:label id="lab_us-gaap_InterestPaid_label_en-US" xlink:label="lab_us-gaap_InterestPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Including Capitalized Interest, Operating and Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaid" xlink:to="lab_us-gaap_InterestPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019ff14a-1b48-7410-92ae-64b4bf3a4edf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (Loss)</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019ff14a-1b48-7650-8126-ff960c0123cd_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_019ff14a-1b48-7fce-9c3a-393be465b4ea_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (Loss)</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_019ff14a-1b49-773a-b0af-d017a7a7e89d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-Sale Securities</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_019ff14a-1aa9-742a-acff-7d5ea8b4edb2_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_019ff14a-1b49-7836-bdb7-a7b7dd845743_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination of commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Origination, Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:to="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PrivateLabelMember_019ff14a-1bcb-777e-9a02-b6de281ea892_terseLabel_en-US" xlink:label="lab_bsprt_PrivateLabelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Label</link:label>
    <link:label id="lab_bsprt_PrivateLabelMember_label_en-US" xlink:label="lab_bsprt_PrivateLabelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Label [Member]</link:label>
    <link:label id="lab_bsprt_PrivateLabelMember_documentation_en-US" xlink:label="lab_bsprt_PrivateLabelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Label</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PrivateLabelMember" xlink:href="bsprt-20260930.xsd#bsprt_PrivateLabelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PrivateLabelMember" xlink:to="lab_bsprt_PrivateLabelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DurhamNorthCarolina1Member_01a1534f-4fb3-769c-850f-bdca172fa0c3_terseLabel_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Durham, NC</link:label>
    <link:label id="lab_bsprt_DurhamNorthCarolina1Member_label_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Durham, North Carolina 1 [Member]</link:label>
    <link:label id="lab_bsprt_DurhamNorthCarolina1Member_documentation_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Durham, North Carolina 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DurhamNorthCarolina1Member" xlink:href="bsprt-20260930.xsd#bsprt_DurhamNorthCarolina1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DurhamNorthCarolina1Member" xlink:to="lab_bsprt_DurhamNorthCarolina1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_019ff14a-1aa9-7e1f-bf29-867000d31144_terseLabel_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial risk rating</link:label>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_label_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial Risk Rating Of Loans</link:label>
    <link:label id="lab_bsprt_InitialRiskRatingOfLoans_documentation_en-US" xlink:label="lab_bsprt_InitialRiskRatingOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial Risk Rating of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InitialRiskRatingOfLoans" xlink:href="bsprt-20260930.xsd#bsprt_InitialRiskRatingOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InitialRiskRatingOfLoans" xlink:to="lab_bsprt_InitialRiskRatingOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_019ff14a-1b48-7819-ba01-f95a924ad0bd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers into Level III</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_019ff14a-1b49-7bf0-89e6-b89d61f7e5f5_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charge offs from specific allowance for credit losses</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-Off</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOff_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateChargeOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:to="lab_bsprt_MortgageLoansOnRealEstateChargeOff" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019ff14a-1b48-75ed-9756-095f26552cfa_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LicensingAgreementsMember_019ff14a-1aa9-799c-b26a-6698353203fe_terseLabel_en-US" xlink:label="lab_us-gaap_LicensingAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Licensing Agreements</link:label>
    <link:label id="lab_us-gaap_LicensingAgreementsMember_label_en-US" xlink:label="lab_us-gaap_LicensingAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Licensing Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LicensingAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LicensingAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LicensingAgreementsMember" xlink:to="lab_us-gaap_LicensingAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_019ff14a-1bcb-7ab1-92ed-c295afc2d380_periodStartLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Non-performing loan amortized cost at beginning of year, January 1</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_019ff14a-1bcb-787c-9b87-7d247ea95a92_periodEndLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Non-performing loan amortized cost end of period</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_019ff14a-1b49-706d-9747-467b4e46dc47_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_019ff14a-1c3c-7dff-a0e4-1ce84d9b3532_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramDomain" xlink:to="lab_srt_ShareRepurchaseProgramDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019ff14a-1bcb-7cd1-8732-0932e92e3322_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic weighted average shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019ff14a-1bcb-7389-9a54-aaefd3589b23_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding for basic earnings per share (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RockyMountainMember_019ff14a-1b49-77aa-b241-9db3ab2e6b4a_terseLabel_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rocky Mountain</link:label>
    <link:label id="lab_bsprt_RockyMountainMember_label_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rocky Mountain [Member]</link:label>
    <link:label id="lab_bsprt_RockyMountainMember_documentation_en-US" xlink:label="lab_bsprt_RockyMountainMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rocky Mountain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RockyMountainMember" xlink:href="bsprt-20260930.xsd#bsprt_RockyMountainMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RockyMountainMember" xlink:to="lab_bsprt_RockyMountainMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_019ff14a-1c3b-7923-b883-765998263462_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Costs Incurred From Arrangements with Advisor and Affiliates</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebt_019ff14a-1b49-7bdd-8f92-d617682c9ef1_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_SecuredDebt_label_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebt" xlink:to="lab_us-gaap_SecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_019ff14a-1bcb-75c9-8aa2-53d4517e0380_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_019ff14a-1aa9-74a3-8d5c-f9f3de7e8bcc_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019ff14a-1bcb-7ce3-a928-697d032e3768_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_019ff14a-1aa9-778f-9b32-198261787ac7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRecordedInvestmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:to="lab_us-gaap_FinancingReceivableRecordedInvestmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_019ff14a-1aa9-79ff-80b8-eae1eda19414_terseLabel_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded</link:label>
    <link:label id="lab_us-gaap_UnfundedLoanCommitmentMember_label_en-US" xlink:label="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unfunded Loan Commitment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnfundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnfundedLoanCommitmentMember" xlink:to="lab_us-gaap_UnfundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_MD_019ff14a-1b49-7750-9618-6d487c68f732_terseLabel_en-US" xlink:label="lab_stpr_MD" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maryland</link:label>
    <link:label id="lab_stpr_MD_label_en-US" xlink:label="lab_stpr_MD" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MARYLAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_MD" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_MD"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_MD" xlink:to="lab_stpr_MD" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FarWestMember_019ff14a-1bcb-7208-8b29-713705478ca5_terseLabel_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Far West</link:label>
    <link:label id="lab_bsprt_FarWestMember_label_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Far West [Member]</link:label>
    <link:label id="lab_bsprt_FarWestMember_documentation_en-US" xlink:label="lab_bsprt_FarWestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Far West</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FarWestMember" xlink:href="bsprt-20260930.xsd#bsprt_FarWestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FarWestMember" xlink:to="lab_bsprt_FarWestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestInJointVentures_019ff14a-1b49-7878-a7ef-ecd97c05de05_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestInJointVentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest in joint ventures</link:label>
    <link:label id="lab_us-gaap_MinorityInterestInJointVentures_label_en-US" xlink:label="lab_us-gaap_MinorityInterestInJointVentures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest in Joint Ventures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestInJointVentures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestInJointVentures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestInJointVentures" xlink:to="lab_us-gaap_MinorityInterestInJointVentures" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_019ff14a-1b49-7ce7-b53c-cf61df7d1b59_terseLabel_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale commitments</link:label>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_label_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forward Sale Commitments [Member]</link:label>
    <link:label id="lab_bsprt_ForwardSaleCommitmentsMember_documentation_en-US" xlink:label="lab_bsprt_ForwardSaleCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Forward Sale Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ForwardSaleCommitmentsMember" xlink:href="bsprt-20260930.xsd#bsprt_ForwardSaleCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ForwardSaleCommitmentsMember" xlink:to="lab_bsprt_ForwardSaleCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_019ff14a-1b49-73d6-ab89-3bda5b2bfa38_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Interest Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_019ff14a-1bcb-78f7-962a-8b1c151412ff_terseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, Held for Investment</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:to="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019ff14a-1bcb-7237-ab49-ae96e2b139d2_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019ff14a-1b48-75fb-b857-6c58de0c08f3_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Accounting</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019ff14a-1bcb-7d0e-b195-0e753a533181_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_019ff14a-1bcb-7d92-9277-86f45b5ecb0f_terseLabel_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DRIP</link:label>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_label_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend Reinvestment And Direct Stock Purchase Plan (DRIP) [Member]</link:label>
    <link:label id="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember_documentation_en-US" xlink:label="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividend Reinvestment And Direct Stock Purchase Plan (DRIP)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:href="bsprt-20260930.xsd#bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:to="lab_bsprt_DividendReinvestmentAndDirectStockPurchasePlanDRIPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_019ff14a-1bcb-7ec4-824f-9f0c2c5f2c9f_negatedTerseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized (gain)/loss on sale of available for sale securities, measured at fair value</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Trading, Gain (Loss)</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Trading, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleTradingGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019ff14a-1b48-723a-8729-d899383a98c3_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Basic net income/(loss) applicable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019ff14a-1b48-7553-aa0b-ef840e9669e3_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic net income/(loss) applicable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019ff14a-1b49-7df4-bc73-29f44ca1adcd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity_019ff14a-1aa9-7a65-bcf8-658a5868e16d_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Days to Maturity</link:label>
    <link:label id="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity_label_en-US" xlink:label="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Weighted Average Days To Maturity</link:label>
    <link:label id="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Weighted Average Days To Maturity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:href="bsprt-20260930.xsd#bsprt_DebtInstrumentWeightedAverageDaysToMaturity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:to="lab_bsprt_DebtInstrumentWeightedAverageDaysToMaturity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019ff14a-1aa9-7701-b6ed-c1781dd079dd_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repo and revolving credit facilities, commercial mortgage loans, capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements_019ff14a-1b49-7553-b81a-377aeecc0b3e_negatedTerseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net borrowings/(paydowns) on repurchase agreements - real estate securities, less than 90 days maturity</link:label>
    <link:label id="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements_label_en-US" xlink:label="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From (Repayment Of) Real Estate Security Repurchase Agreements</link:label>
    <link:label id="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from Real Estate Security Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:href="bsprt-20260930.xsd#bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:to="lab_bsprt_ProceedsFromRepaymentOfRealEstateSecurityRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StraightLineRent_019ff14a-1c3b-7cb2-b23a-5de46d2f3413_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StraightLineRent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Straight line rental income</link:label>
    <link:label id="lab_us-gaap_StraightLineRent_label_en-US" xlink:label="lab_us-gaap_StraightLineRent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Straight Line Rent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StraightLineRent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StraightLineRent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StraightLineRent" xlink:to="lab_us-gaap_StraightLineRent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019ff14a-1b49-7a96-bdd5-5698f4c6a090_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment, net of allowance for credit losses of $71,932 and $38,302 as of September&#160;30, 2026 and December&#160;31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019ff14a-1b49-7980-808a-a87f0d51687e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total commercial mortgage loans, held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_019ff14a-1b49-772f-91c0-3051fe346f9a_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total commercial mortgage loans, held for investment, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_019ff14a-1b48-7e48-b39a-99e6845e94cd_negatedLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net unrealized loss on CLO bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Net Unrealized Gain (Loss), before Tax</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Net Unrealized Gain (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleAccumulatedNetUnrealizedGainLossBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_019ff14a-1bcb-7cf3-888a-a1e77a72a255_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for loss sharing</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Allowance for Loss Sharing</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Allowance for Loss Sharing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedAllowanceForLossSharing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019ff14a-1bcb-7dcd-8fb0-649e37838b5b_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Issued Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_019ff14a-1b49-72ac-90aa-8aea2376d703_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_019ff14a-1c3b-7129-85d4-73becba7688a_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Controlling Interest</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BridgeMember_019ff14a-1b48-7b29-9bc9-e708fb5ef04b_terseLabel_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bridge</link:label>
    <link:label id="lab_bsprt_BridgeMember_label_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bridge [Member]</link:label>
    <link:label id="lab_bsprt_BridgeMember_documentation_en-US" xlink:label="lab_bsprt_BridgeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bridge</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BridgeMember" xlink:href="bsprt-20260930.xsd#bsprt_BridgeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BridgeMember" xlink:to="lab_bsprt_BridgeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019ff14a-1bcb-7d45-914b-ec1024989c11_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_019ff14a-1c3b-7c92-a624-933fdc6a14f8_totalLabel_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) applicable to common stock, basic</link:label>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_label_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic, Including Undistributed Earnings (Loss) Allocated to Participating Securities</link:label>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_documentation_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic, Including Undistributed Earnings (Loss) Allocated to Participating Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:href="bsprt-20260930.xsd#bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:to="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersBasicIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_019ff14a-1b49-721b-9dfc-5931eba6f4d9_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_019ff14a-1b48-7f8b-9e48-d0a6d983541b_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock issued under dividend reinvestment plan (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Dividend Reinvestment Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesDividendReinvestmentPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019ff14a-1bcb-7abe-9254-697230977f67_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt, amount outstanding</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019ff14a-1bcb-7a0e-b651-069483ee7ecd_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding principal</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionRate_019ff14a-1bcb-7b91-bfac-0cd16b07bbd1_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction rate (percent)</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionRate_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionRate" xlink:to="lab_us-gaap_RelatedPartyTransactionRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member_019ff14a-1c3b-770c-b525-168a9b2bc28e_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024-FL11 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2023-FL10 [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2023-FL10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:href="bsprt-20260930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2023FL10Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_019ff14a-1b49-7629-b417-f822b0e82c1c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year three, originated in prior fiscal year two</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_019ff14a-1b48-7209-8ee2-728b1eff17bb_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage impairment insurance</link:label>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_019ff14a-1b48-7b42-8f8d-cee7f901caed_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR impairment</link:label>
    <link:label id="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery_label_en-US" xlink:label="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights (MSR) Impairment (Recovery)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageServicingRightsMSRImpairmentRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:to="lab_us-gaap_MortgageServicingRightsMSRImpairmentRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_019ff14a-1bcb-753d-9282-485993e9a807_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Loaned or Sold under Agreements to Repurchase, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:to="lab_us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019ff14a-1b49-7bcb-818c-13ed93eb63f8_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_019ff14a-1bcb-7fb8-bb7d-d71849795d71_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Collateral</link:label>
    <link:label id="lab_us-gaap_DerivativeCollateralObligationToReturnCash_label_en-US" xlink:label="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Collateral, Obligation to Return Cash Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:to="lab_us-gaap_DerivativeCollateralObligationToReturnCash" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration_019ff14a-1b49-7cb0-81c1-b30104df5a35_terseLabel_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock converted to common stock, per share stock consideration (in shares)</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration_label_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock Converted To Common Stock, Per Share Stock Consideration</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration_documentation_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock Converted To Common Stock, Per Share Stock Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:href="bsprt-20260930.xsd#bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:to="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockPerShareStockConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019ff14a-1aa9-7b1e-83b3-e65fcf959ea5_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock and Equity Transactions</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019ff14a-1b48-7547-933e-1e529146fe63_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_019ff14a-1bcb-7579-92ae-4174c2f2ecf8_totalLabel_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders' equity</link:label>
    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_label_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Assets, Equity, Attributable to Parent</link:label>
    <link:label id="lab_bsprt_NetAssetsEquityAttributableToParent_documentation_en-US" xlink:label="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Assets, Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetAssetsEquityAttributableToParent" xlink:href="bsprt-20260930.xsd#bsprt_NetAssetsEquityAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetAssetsEquityAttributableToParent" xlink:to="lab_bsprt_NetAssetsEquityAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PortlandOregonMember_019ff14a-1bcb-73df-ae51-e2f8c3544f20_terseLabel_en-US" xlink:label="lab_bsprt_PortlandOregonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portland, OR</link:label>
    <link:label id="lab_bsprt_PortlandOregonMember_label_en-US" xlink:label="lab_bsprt_PortlandOregonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portland, Oregon [Member]</link:label>
    <link:label id="lab_bsprt_PortlandOregonMember_documentation_en-US" xlink:label="lab_bsprt_PortlandOregonMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Portland, Oregon</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PortlandOregonMember" xlink:href="bsprt-20260930.xsd#bsprt_PortlandOregonMember"/>
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    <link:label id="lab_us-gaap_CreditLossStatusDomain_019ff14a-1b48-7125-a5f2-843f6a55b666_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditLossStatusDomain_label_en-US" xlink:label="lab_us-gaap_CreditLossStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditLossStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossStatusDomain" xlink:to="lab_us-gaap_CreditLossStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AffordableMember_019ff14a-1b49-732f-aedc-481609154909_terseLabel_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affordable</link:label>
    <link:label id="lab_bsprt_AffordableMember_label_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affordable [Member]</link:label>
    <link:label id="lab_bsprt_AffordableMember_documentation_en-US" xlink:label="lab_bsprt_AffordableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Affordable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AffordableMember" xlink:href="bsprt-20260930.xsd#bsprt_AffordableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AffordableMember" xlink:to="lab_bsprt_AffordableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019ff14a-1bcb-7486-870d-afeef514600b_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_019ff14a-1c3b-7995-9f51-9f3663ab1032_terseLabel_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Modification accounted for as repayment and new loan</link:label>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_label_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Modification Accounted For As Repayment And New Loan</link:label>
    <link:label id="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan_documentation_en-US" xlink:label="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Modification Accounted For As Repayment And New Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:href="bsprt-20260930.xsd#bsprt_ModificationAccountedForAsRepaymentAndNewLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:to="lab_bsprt_ModificationAccountedForAsRepaymentAndNewLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_019ff14a-1b49-75be-b39c-01e70cc4d20d_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, held for sale</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_019ff14a-1b49-781f-9a1a-529038a32ef1_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets, Net</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_label_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateHeldforsale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateHeldforsale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateHeldforsale" xlink:to="lab_us-gaap_RealEstateHeldforsale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_019ff14a-1c3b-7d2d-8cfe-256d173032d3_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reserved for issuance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherRealEstatePropertyMember_019ff14a-1bcb-7596-96dc-aafbc6c54b36_terseLabel_en-US" xlink:label="lab_bsprt_OtherRealEstatePropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_bsprt_OtherRealEstatePropertyMember_label_en-US" xlink:label="lab_bsprt_OtherRealEstatePropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate Property [Member]</link:label>
    <link:label id="lab_bsprt_OtherRealEstatePropertyMember_documentation_en-US" xlink:label="lab_bsprt_OtherRealEstatePropertyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Real Estate Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherRealEstatePropertyMember" xlink:href="bsprt-20260930.xsd#bsprt_OtherRealEstatePropertyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherRealEstatePropertyMember" xlink:to="lab_bsprt_OtherRealEstatePropertyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_019ff14a-1c3c-73b3-b5c4-338881dc513f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019ff14a-1b48-783d-ae59-f0d8c11cf731_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_019ff14a-1aa9-7f29-a9d1-a21e5fb62f60_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net of amortization</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure_019ff14a-1c3b-7a66-85e2-cba3038adfee_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Security, Mortgage-Backed, Held-to-Maturity, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:to="lab_us-gaap_MortgageBackedSecuritiesHeldToMaturityFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet_01a15fd3-ed57-715a-919f-c6ce7f58904f_terseLabel_en-US" xlink:label="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation (in shares)</link:label>
    <link:label id="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet_label_en-US" xlink:label="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Granted, Shares, Share-Based Payment Arrangement, after Forfeiture, Net</link:label>
    <link:label id="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet_documentation_en-US" xlink:label="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Granted, Shares, Share-Based Payment Arrangement, after Forfeiture, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:href="bsprt-20260930.xsd#bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:to="lab_bsprt_SharesGrantedSharesShareBasedPaymentArrangementAfterForfeitureNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_019ff14a-1b48-715d-8f1e-80f5cd9e5493_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_019ff14a-1b49-71c2-845a-3932d4cdbca3_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-lived intangible, carrying value</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Excluding Goodwill, Indefinite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BenefitStreetPartnersLLCMember_019ff14a-1b49-7cc9-adad-3aaa0030c0d8_terseLabel_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit Street Partners LLC</link:label>
    <link:label id="lab_bsprt_BenefitStreetPartnersLLCMember_label_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefit Street Partners LLC [Member]</link:label>
    <link:label id="lab_bsprt_BenefitStreetPartnersLLCMember_documentation_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Benefit Street Partners LLC [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BenefitStreetPartnersLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_BenefitStreetPartnersLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BenefitStreetPartnersLLCMember" xlink:to="lab_bsprt_BenefitStreetPartnersLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_019ff14a-1b49-750b-bf7e-0636c8f0a487_terseLabel_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC</link:label>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_label_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC [Member]</link:label>
    <link:label id="lab_bsprt_RiverwalkAkerBSPVentureLLCMember_documentation_en-US" xlink:label="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Riverwalk Aker BSP Venture LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_RiverwalkAkerBSPVentureLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:to="lab_bsprt_RiverwalkAkerBSPVentureLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary_019ff14a-1bcb-72cc-b9a6-832d33ea37bc_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceOnThirdAnniversary" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireFinanceReceivables_019ff14a-1aa9-71a4-9d7e-bef1514a2b73_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Origination and purchase of commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireFinanceReceivables_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Finance Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireFinanceReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:to="lab_us-gaap_PaymentsToAcquireFinanceReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax_019ff14a-1bcb-71ae-b36a-8de6ed8e9e5a_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total unrealized gain (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_019ff14a-1bcb-7ded-882f-9e36eb1cbf3c_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain/(Loss)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:to="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_019ff14a-1b49-73cf-9f74-5204867465a3_negatedTerseLabel_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Gain)/loss from other real estate investments</link:label>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_label_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) On Other Real Estate Owned</link:label>
    <link:label id="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned_documentation_en-US" xlink:label="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change in Unrealized Gain (Loss) on Other Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:href="bsprt-20260930.xsd#bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:to="lab_bsprt_ChangeinUnrealizedGainLossOnOtherRealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019ff14a-1b49-73b2-98d7-e5c51d05b0c0_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest, ownership percentage by parent</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_TaxableREITSubsidiariesMember_019ff14a-1aa9-7d4b-a993-64d16919b21b_terseLabel_en-US" xlink:label="lab_bsprt_TaxableREITSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conduit</link:label>
    <link:label id="lab_bsprt_TaxableREITSubsidiariesMember_label_en-US" xlink:label="lab_bsprt_TaxableREITSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxable REIT Subsidiaries [Member]</link:label>
    <link:label id="lab_bsprt_TaxableREITSubsidiariesMember_documentation_en-US" xlink:label="lab_bsprt_TaxableREITSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Taxable REIT Subsidiaries [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_TaxableREITSubsidiariesMember" xlink:href="bsprt-20260930.xsd#bsprt_TaxableREITSubsidiariesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_TaxableREITSubsidiariesMember" xlink:to="lab_bsprt_TaxableREITSubsidiariesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_019ff14a-1aa9-7340-9958-e19ba85af55f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncompeteAgreementsMember_019ff14a-1bcb-7b27-b4af-4ee35c714dfa_terseLabel_en-US" xlink:label="lab_us-gaap_NoncompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-compete Agreements</link:label>
    <link:label id="lab_us-gaap_NoncompeteAgreementsMember_label_en-US" xlink:label="lab_us-gaap_NoncompeteAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncompete Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncompeteAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncompeteAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncompeteAgreementsMember" xlink:to="lab_us-gaap_NoncompeteAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_019ff14a-1b49-7bb1-993d-cf3f4607e3bc_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_019ff14a-1bcb-75a6-9342-537a4c5488ce_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity interest acquired, percentage</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Voting Equity Interest Acquired, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="lab_us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019ff14a-1b48-73a0-a334-3ac065fdc839_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted weighted average shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019ff14a-1b48-7d5f-b066-1c4ddd968f0a_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average common shares outstanding for diluted earnings per share (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SoutheastMember_019ff14a-1b48-746b-8995-067d5a59d6ac_terseLabel_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Southeast</link:label>
    <link:label id="lab_bsprt_SoutheastMember_label_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Southeast [Member]</link:label>
    <link:label id="lab_bsprt_SoutheastMember_documentation_en-US" xlink:label="lab_bsprt_SoutheastMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Southeast</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SoutheastMember" xlink:href="bsprt-20260930.xsd#bsprt_SoutheastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SoutheastMember" xlink:to="lab_bsprt_SoutheastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_019ff14a-1b49-7378-928a-24b77190b15e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_label_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019ff14a-1b49-7d32-a0c6-7e9de382ceab_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_019ff14a-1bcb-7f66-8063-2d7be7a9fe8c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-7cf5-804e-7a72fadda828_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total gross carrying value of loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-7631-af9f-4a1bef6171f8_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_019ff14a-1b49-79ea-8013-c8c5740b4fc8_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Amortized Cost</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, before Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestBeforeAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019ff14a-1bcb-7413-be6e-87e54be91944_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_019ff14a-1b49-713f-985b-f41694966fd9_terseLabel_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate</link:label>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_label_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_JeffersonvilleJVAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jeffersonville JV, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JeffersonvilleJVAffiliateMember" xlink:href="bsprt-20260930.xsd#bsprt_JeffersonvilleJVAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JeffersonvilleJVAffiliateMember" xlink:to="lab_bsprt_JeffersonvilleJVAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust_019ff14a-1c3b-70dd-907c-469e389afc46_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment to acquire interest in CMBS trust</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust_label_en-US" xlink:label="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Interest In Variable Interest Entity, CMBS Trust</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust_documentation_en-US" xlink:label="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Interest In Variable Interest Entity, CMBS Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:href="bsprt-20260930.xsd#bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:to="lab_bsprt_PaymentsToAcquireInterestInVariableInterestEntityCMBSTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019ff14a-1aa9-78c4-95c8-a3b82551535b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_019ff14a-1bcb-7578-9e40-2d0f16dc3a51_netLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_019ff14a-1bcb-7ec7-8629-b3c9eacea2b7_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_019ff14a-1bcb-729a-821d-3508b6ae26bf_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CML, HFS, measured at fair value - Non-Agency</link:label>
    <link:label id="lab_us-gaap_MortgageReceivablesMember_label_en-US" xlink:label="lab_us-gaap_MortgageReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgageReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageReceivablesMember" xlink:to="lab_us-gaap_MortgageReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MezzanineLoansMember_019ff14a-1bcb-718f-89c5-8f96f6c401ea_terseLabel_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mezzanine loans</link:label>
    <link:label id="lab_bsprt_MezzanineLoansMember_label_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mezzanine Loans [Member]</link:label>
    <link:label id="lab_bsprt_MezzanineLoansMember_documentation_en-US" xlink:label="lab_bsprt_MezzanineLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mezzanine Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MezzanineLoansMember" xlink:href="bsprt-20260930.xsd#bsprt_MezzanineLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MezzanineLoansMember" xlink:to="lab_bsprt_MezzanineLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_019ff14a-1bcb-7c75-9a03-10b6f7ef226c_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_019ff14a-1bcb-75be-9999-bdcc062780f2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Gross Amounts of Recognized Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FundedLoanCommitmentMember_019ff14a-1c3b-7f21-bf57-97981980d7aa_terseLabel_en-US" xlink:label="lab_bsprt_FundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funded</link:label>
    <link:label id="lab_bsprt_FundedLoanCommitmentMember_label_en-US" xlink:label="lab_bsprt_FundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funded Loan Commitment [Member]</link:label>
    <link:label id="lab_bsprt_FundedLoanCommitmentMember_documentation_en-US" xlink:label="lab_bsprt_FundedLoanCommitmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Funded Loan Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FundedLoanCommitmentMember" xlink:href="bsprt-20260930.xsd#bsprt_FundedLoanCommitmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FundedLoanCommitmentMember" xlink:to="lab_bsprt_FundedLoanCommitmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_VA_019ff14a-1b49-7b35-80f1-392b8949423a_terseLabel_en-US" xlink:label="lab_stpr_VA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Virginia</link:label>
    <link:label id="lab_stpr_VA_label_en-US" xlink:label="lab_stpr_VA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">VIRGINIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_VA" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_VA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_VA" xlink:to="lab_stpr_VA" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery_019ff14a-1c3b-7d59-997d-d03b9948684a_negatedTerseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cost recovery</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Cost Recovery</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Cost Recovery</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestCostRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal_019ff14a-1bcb-7e26-b5f1-7906763bdfe5_terseLabel_en-US" xlink:label="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment reversal</link:label>
    <link:label id="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal_label_en-US" xlink:label="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Impairment Reversal</link:label>
    <link:label id="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal_documentation_en-US" xlink:label="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Impairment Reversal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:href="bsprt-20260930.xsd#bsprt_ServicingAssetAtAmortizedCostImpairmentReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:to="lab_bsprt_ServicingAssetAtAmortizedCostImpairmentReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019ff14a-1bcb-7fbf-b827-06ad9fd3fb6f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating5Member_019ff14a-1bcb-7559-b1f6-9083cee3d944_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5</link:label>
    <link:label id="lab_bsprt_InvestmentRating5Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 5 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating5Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating5Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 5 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating5Member" xlink:href="bsprt-20260930.xsd#bsprt_InvestmentRating5Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating5Member" xlink:to="lab_bsprt_InvestmentRating5Member" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_019ff14a-1c3b-736a-bf58-a44b0b1b06b5_terseLabel_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and beyond</link:label>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Four</link:label>
    <link:label id="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:href="bsprt-20260930.xsd#bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_bsprt_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfUnsecuredDebt_019ff14a-1c3b-7547-8aa1-ff8965db56ae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of unsecured debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfUnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfUnsecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_01a164e0-ebf0-7fcf-b440-f003ddb34e44_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Net Amount of Liabilities Presented on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GinneMaeMember_019ff14a-1aa8-7e20-9260-8bc6d14f9f39_terseLabel_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ginnie Mae</link:label>
    <link:label id="lab_bsprt_GinneMaeMember_label_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ginne Mae [Member]</link:label>
    <link:label id="lab_bsprt_GinneMaeMember_documentation_en-US" xlink:label="lab_bsprt_GinneMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ginne Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GinneMaeMember" xlink:href="bsprt-20260930.xsd#bsprt_GinneMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GinneMaeMember" xlink:to="lab_bsprt_GinneMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_019ff14a-1aa8-7093-90e7-cae535ddbc24_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowings on unsecured debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfUnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AustinTexasMember_01a138a7-3c14-7ad7-85f6-a1b4ff8872e7_terseLabel_en-US" xlink:label="lab_bsprt_AustinTexasMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Austin, TX</link:label>
    <link:label id="lab_bsprt_AustinTexasMember_label_en-US" xlink:label="lab_bsprt_AustinTexasMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Austin, Texas [Member]</link:label>
    <link:label id="lab_bsprt_AustinTexasMember_documentation_en-US" xlink:label="lab_bsprt_AustinTexasMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Austin, Texas</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AustinTexasMember" xlink:href="bsprt-20260930.xsd#bsprt_AustinTexasMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AustinTexasMember" xlink:to="lab_bsprt_AustinTexasMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_019ff14a-1b49-72a9-a1d1-59ddc12f5432_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_019ff14a-1aa9-7c3a-85a9-7b76982e715c_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019ff14a-1b49-728d-ab21-69ead9cb4e80_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Lease Payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingAbstract" xlink:to="lab_us-gaap_TransfersAndServicingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_019ff14a-1b48-7cb8-b569-bbef386934cf_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssetsAndLiabilitiesNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ReferralFeeIncomeMember_019ff14a-1b49-797d-aa39-c9a4d3443638_terseLabel_en-US" xlink:label="lab_bsprt_ReferralFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Referral fee income</link:label>
    <link:label id="lab_bsprt_ReferralFeeIncomeMember_label_en-US" xlink:label="lab_bsprt_ReferralFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Referral Fee Income [Member]</link:label>
    <link:label id="lab_bsprt_ReferralFeeIncomeMember_documentation_en-US" xlink:label="lab_bsprt_ReferralFeeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Referral Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ReferralFeeIncomeMember" xlink:href="bsprt-20260930.xsd#bsprt_ReferralFeeIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ReferralFeeIncomeMember" xlink:to="lab_bsprt_ReferralFeeIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019ff14a-1c3c-7247-9823-028f90f157eb_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_019ff14a-1b48-7009-af0d-1a51f798b1ab_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of cash, cash equivalents and restricted cash:</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_019ff14a-1aa9-7741-ba4d-fa012356c16b_terseLabel_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate</link:label>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_label_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_WalgreensJVAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_WalgreensJVAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Walgreens JV, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WalgreensJVAffiliateMember" xlink:href="bsprt-20260930.xsd#bsprt_WalgreensJVAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WalgreensJVAffiliateMember" xlink:to="lab_bsprt_WalgreensJVAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue_019ff14a-1bcb-7c60-a5d9-2e007942efe5_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Addition of non-performing loan amortized cost</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Additions Of Carrying Value</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual, Additions Of Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestNonaccrualAdditionsOfCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_019ff14a-1aa9-7044-818d-37a2e1073fc6_negatedTerseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Principal charge-off</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-offs</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateChargeOffs_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Charge-offs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateChargeOffs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:to="lab_bsprt_MortgageLoansOnRealEstateChargeOffs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019ff14a-1b49-77df-bd93-d045f9201dc6_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_019ff14a-1bcb-7e39-8e24-203883e16561_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019ff14a-1b49-7d3f-9dcd-61f2f5d5d9de_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019ff14a-1bcb-76a3-bb98-a55d5632ae77_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue_019ff14a-1bcb-7464-85de-8e2973e491e7_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investment, quoted market value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Quoted Market Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentQuotedMarketValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:to="lab_us-gaap_EquityMethodInvestmentQuotedMarketValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentInterestRateFloor_019ff14a-1b49-77eb-82fe-ce9925ab3d4c_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentInterestRateFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Floor</link:label>
    <link:label id="lab_bsprt_DebtInstrumentInterestRateFloor_label_en-US" xlink:label="lab_bsprt_DebtInstrumentInterestRateFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Floor</link:label>
    <link:label id="lab_bsprt_DebtInstrumentInterestRateFloor_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentInterestRateFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentInterestRateFloor" xlink:href="bsprt-20260930.xsd#bsprt_DebtInstrumentInterestRateFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentInterestRateFloor" xlink:to="lab_bsprt_DebtInstrumentInterestRateFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_019ff14a-1bcb-7de0-97f9-2d792052e13b_terseLabel_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement</link:label>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_label_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement [Member]</link:label>
    <link:label id="lab_bsprt_ThirdPartyVendorAgreementMember_documentation_en-US" xlink:label="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Vendor Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ThirdPartyVendorAgreementMember" xlink:href="bsprt-20260930.xsd#bsprt_ThirdPartyVendorAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ThirdPartyVendorAgreementMember" xlink:to="lab_bsprt_ThirdPartyVendorAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019ff14a-1b49-7f87-80b3-6ee97ea20d28_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019ff14a-1b49-789d-a49f-e37ea2184ad0_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, at fair value</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1_019ff14a-1b49-747d-9fbd-d45d6cc165de_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtAmortizedValueAmortization1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:to="lab_us-gaap_ServicingAssetAtAmortizedValueAmortization1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_019ff14a-1c3b-74bb-be29-4c00e286666c_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Variable Interest Entities Assets and Liabilities, at Fair Value</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:to="lab_us-gaap_VariableInterestEntityDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_019ff14a-1b48-72c7-ba0c-ee74300ccdfc_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtAssumptionOnRepurchasesAgreements_019ff14a-1c3b-7cff-ba25-8fb7a4595693_terseLabel_en-US" xlink:label="lab_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt assumption on repurchases agreements</link:label>
    <link:label id="lab_bsprt_DebtAssumptionOnRepurchasesAgreements_label_en-US" xlink:label="lab_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Assumption On Repurchases Agreements</link:label>
    <link:label id="lab_bsprt_DebtAssumptionOnRepurchasesAgreements_documentation_en-US" xlink:label="lab_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Assumption On Repurchases Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:href="bsprt-20260930.xsd#bsprt_DebtAssumptionOnRepurchasesAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:to="lab_bsprt_DebtAssumptionOnRepurchasesAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_019ff14a-1bcb-787c-a18b-1bf2d1655429_terseLabel_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Santander Securities</link:label>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_label_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Santander Securities [Member]</link:label>
    <link:label id="lab_bsprt_SantanderSecuritiesMember_documentation_en-US" xlink:label="lab_bsprt_SantanderSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Santander Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SantanderSecuritiesMember" xlink:href="bsprt-20260930.xsd#bsprt_SantanderSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SantanderSecuritiesMember" xlink:to="lab_bsprt_SantanderSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_019ff14a-1bcb-785f-aff8-f5eeba960a8c_totalLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, at fair value</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_019ff14a-1bcb-765a-8925-6292376177f6_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payables due to affiliate</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsCommonStock_019ff14a-1b49-7633-93fe-8df6105e0a0f_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock distributions</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStock" xlink:to="lab_us-gaap_DividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019ff14a-1aa8-75ba-baec-6c6df3f6d4c3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_019ff14a-1c3b-70cb-897d-38a85545e9b0_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:label id="lab_us-gaap_RealEstateOwnedTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateOwnedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOwnedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateOwnedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOwnedTextBlock" xlink:to="lab_us-gaap_RealEstateOwnedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PartnershipUnitToCommonStockConversionRatio_019ff14a-1c3c-7c8e-a876-f512f18a6456_terseLabel_en-US" xlink:label="lab_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unit to common stock conversion ratio</link:label>
    <link:label id="lab_bsprt_PartnershipUnitToCommonStockConversionRatio_label_en-US" xlink:label="lab_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partnership Unit To Common Stock Conversion Ratio</link:label>
    <link:label id="lab_bsprt_PartnershipUnitToCommonStockConversionRatio_documentation_en-US" xlink:label="lab_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Partnership Unit To Common Stock Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:href="bsprt-20260930.xsd#bsprt_PartnershipUnitToCommonStockConversionRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:to="lab_bsprt_PartnershipUnitToCommonStockConversionRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019ff14a-1aa9-74cd-af96-66f87836882d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_019ff14a-1bcb-70c2-9a86-37e568507e97_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investment property, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateInvestmentPropertyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019ff14a-1b48-77f8-9685-0b487b408f34_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForLossSharing_019ff14a-1bcb-7702-a80d-9683da3ab2ea_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for loss sharing</link:label>
    <link:label id="lab_bsprt_AllowanceForLossSharing_label_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance For Loss Sharing</link:label>
    <link:label id="lab_bsprt_AllowanceForLossSharing_documentation_en-US" xlink:label="lab_bsprt_AllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance For Loss Sharing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForLossSharing" xlink:href="bsprt-20260930.xsd#bsprt_AllowanceForLossSharing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForLossSharing" xlink:to="lab_bsprt_AllowanceForLossSharing" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_019ff14a-1bcb-7121-85d7-0ac4aabf0870_terseLabel_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_label_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate [Member]</link:label>
    <link:label id="lab_bsprt_September2021MortgageNotePayableAffiliateMember_documentation_en-US" xlink:label="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">September 2021 Mortgage Note Payable, Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:href="bsprt-20260930.xsd#bsprt_September2021MortgageNotePayableAffiliateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:to="lab_bsprt_September2021MortgageNotePayableAffiliateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member_019ff14a-1bcb-7769-aced-b29b516fa2a4_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2025-FL12</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2025-FL12 [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2025-FL12</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:href="bsprt-20260930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2025FL12Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_019ff14a-1bcb-779c-9d38-daa03413dc90_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_019ff14a-1aa9-7fd5-bad9-d002027146f8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019ff14a-1b49-7144-9687-77e372bca491_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_019ff14a-1c3b-7b3e-84cd-f5d4b4b3e4cd_verboseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Beginning of period, authorized repurchase amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest_019ff14a-1b49-75c8-8b94-7b09dea1f37b_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total purchase consideration</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less), and Goodwill, Less Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedLessNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_019ff14a-1bcb-7df9-ab5a-6c21f2c1d3d2_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_019ff14a-1b48-7742-84d5-180713d3fc78_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Loans, Held for Sale</link:label>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_label_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans, Held for Sale, Measured at Fair Value [Text Block]</link:label>
    <link:label id="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans, Held for Sale, Measured at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:to="lab_bsprt_MortgageLoansHeldForSaleMeasuredAtFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_019ff14a-1bcb-7604-8424-640712d6a909_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2026/stpr-2026.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CMBSTrustMember_019ff14a-1c3c-7216-8904-50bb94bcca12_terseLabel_en-US" xlink:label="lab_bsprt_CMBSTrustMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS Trust</link:label>
    <link:label id="lab_bsprt_CMBSTrustMember_label_en-US" xlink:label="lab_bsprt_CMBSTrustMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CMBS Trust [Member]</link:label>
    <link:label id="lab_bsprt_CMBSTrustMember_documentation_en-US" xlink:label="lab_bsprt_CMBSTrustMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CMBS Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CMBSTrustMember" xlink:href="bsprt-20260930.xsd#bsprt_CMBSTrustMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CMBSTrustMember" xlink:to="lab_bsprt_CMBSTrustMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_019ff14a-1aa9-7c23-b8aa-18603245cf39_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lender Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityAxis" xlink:to="lab_us-gaap_LineOfCreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember_019ff14a-1c3c-7483-b73e-71dff22ba9de_verboseLabel_en-US" xlink:label="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">VIE liabilities, measured at fair value</link:label>
    <link:label id="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember_label_en-US" xlink:label="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">VIE Liabilities, Measured At Fair Value [Member]</link:label>
    <link:label id="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember_documentation_en-US" xlink:label="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">VIE Liabilities, Measured At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:href="bsprt-20260930.xsd#bsprt_VIELiabilitiesMeasuredAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:to="lab_bsprt_VIELiabilitiesMeasuredAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BAMLWHLineOfCreditMember_019ff14a-1aa9-7044-a941-6a7281d562a3_terseLabel_en-US" xlink:label="lab_bsprt_BAMLWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BAML WH Line of Credit</link:label>
    <link:label id="lab_bsprt_BAMLWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_BAMLWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BAML WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_BAMLWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_BAMLWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">BAML WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BAMLWHLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_BAMLWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BAMLWHLineOfCreditMember" xlink:to="lab_bsprt_BAMLWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InitialReturnHurdleRateMember_01a16143-4451-7a8c-9d17-6407a8537e48_terseLabel_en-US" xlink:label="lab_bsprt_InitialReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial Return Hurdle Rate</link:label>
    <link:label id="lab_bsprt_InitialReturnHurdleRateMember_label_en-US" xlink:label="lab_bsprt_InitialReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Initial Return Hurdle Rate [Member]</link:label>
    <link:label id="lab_bsprt_InitialReturnHurdleRateMember_documentation_en-US" xlink:label="lab_bsprt_InitialReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Initial Return Hurdle Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InitialReturnHurdleRateMember" xlink:href="bsprt-20260930.xsd#bsprt_InitialReturnHurdleRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InitialReturnHurdleRateMember" xlink:to="lab_bsprt_InitialReturnHurdleRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_019ff14a-1b49-7dcf-b908-e42fb198ff60_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale or paydown of real estate securities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019ff14a-1b49-72f1-a1ab-24c07b49dc25_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_019ff14a-1b49-79ea-a3aa-2d5dc68f0ed9_netLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_019ff14a-1bcb-7234-8643-b9d46f3a2348_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OptionMember_019ff14a-1b48-7b90-8f13-fa9c1c3a6d02_terseLabel_en-US" xlink:label="lab_us-gaap_OptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_OptionMember_label_en-US" xlink:label="lab_us-gaap_OptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Options Held [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OptionMember" xlink:to="lab_us-gaap_OptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VariableInterestEntityLiabilities_019ff14a-1c3b-7eca-a5ae-3fc789a479ba_terseLabel_en-US" xlink:label="lab_bsprt_VariableInterestEntityLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE liabilities, measured at fair value</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityLiabilities_label_en-US" xlink:label="lab_bsprt_VariableInterestEntityLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Liabilities</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityLiabilities_documentation_en-US" xlink:label="lab_bsprt_VariableInterestEntityLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VariableInterestEntityLiabilities" xlink:href="bsprt-20260930.xsd#bsprt_VariableInterestEntityLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VariableInterestEntityLiabilities" xlink:to="lab_bsprt_VariableInterestEntityLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_019ff14a-1b48-7260-9b5b-1f8a7b5f3f9f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019ff14a-1aa8-77a7-a673-3604a2b633f3_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_019ff14a-1b49-779c-9ef8-10292c97cb32_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans eligible for repurchase</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstatePropertiesDomain_019ff14a-1c3c-7ffd-a4d1-10a2f9db32f2_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate Properties [Domain]</link:label>
    <link:label id="lab_us-gaap_RealEstatePropertiesDomain_label_en-US" xlink:label="lab_us-gaap_RealEstatePropertiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Properties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstatePropertiesDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstatePropertiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstatePropertiesDomain" xlink:to="lab_us-gaap_RealEstatePropertiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_019ff14a-1bcb-7ef4-aeda-efef86160bdd_terseLabel_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other related party expenses</link:label>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_label_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Related Party Expenses [Member]</link:label>
    <link:label id="lab_bsprt_OtherRelatedPartyExpensesMember_documentation_en-US" xlink:label="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Related Party Expenses [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OtherRelatedPartyExpensesMember" xlink:href="bsprt-20260930.xsd#bsprt_OtherRelatedPartyExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OtherRelatedPartyExpensesMember" xlink:to="lab_bsprt_OtherRelatedPartyExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract_019ff14a-1bcb-7fff-afa1-01fb8dafed1a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract_label_en-US" xlink:label="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income, Nonoperating [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherIncomeDisclosureNonoperatingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:to="lab_us-gaap_OtherIncomeDisclosureNonoperatingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfLoans_019ff14a-1aa9-73a5-8218-afd68dbf2015_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_019ff14a-1aa9-7ccb-9d34-d8add4400033_verboseLabel_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of Loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_label_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Loans</link:label>
    <link:label id="lab_bsprt_NumberOfLoans_documentation_en-US" xlink:label="lab_bsprt_NumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Mezzanine Loans Funded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfLoans" xlink:href="bsprt-20260930.xsd#bsprt_NumberOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfLoans" xlink:to="lab_bsprt_NumberOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019ff14a-1c3b-7872-b6e2-fd2b51766400_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAsset_019ff14a-1b49-712a-819f-459da12f754d_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, net</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_019ff14a-1b49-7e80-9a77-f0d3d6e2e500_periodStartLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_019ff14a-1b49-7668-880b-ee6b7ea0200c_periodEndLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_label_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAsset" xlink:to="lab_us-gaap_ServicingAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing_01a164bc-5c3c-7a8c-87ba-3690054b618b_verboseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision/(benefit) for credit losses</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing_label_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal), Including Charge-Off Of The Specific Allowance For Loss Sharing</link:label>
    <link:label id="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal), Including Charge-Off Of The Specific Allowance For Loss Sharing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:to="lab_bsprt_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversalIncludingChargeOffOfTheSpecificAllowanceForLossSharing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019ff14a-1b49-7ad6-b587-b52a6b4542ae_totalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income/(loss)</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_019ff14a-1bcb-7c1c-97b3-4e14f81d9cf3_terseLabel_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_label_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Administrative Services Expenses [Member]</link:label>
    <link:label id="lab_bsprt_AdministrativeServicesExpensesMember_documentation_en-US" xlink:label="lab_bsprt_AdministrativeServicesExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Administrative Services Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AdministrativeServicesExpensesMember" xlink:href="bsprt-20260930.xsd#bsprt_AdministrativeServicesExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AdministrativeServicesExpensesMember" xlink:to="lab_bsprt_AdministrativeServicesExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions_019ff14a-1b48-7b54-a539-084488ca8002_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of positions with net unrealized gain (loss) period less than 12 months</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Net Unrealized Gain (Loss) Position, Number of Positions</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Net Unrealized Gain (Loss) Position, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleNetUnrealizedGainLossPositionNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings_019ff14a-1c3c-769e-9eda-5ea36b7f77d2_terseLabel_en-US" xlink:label="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured borrowings from CMBS Trust</link:label>
    <link:label id="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings_label_en-US" xlink:label="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance CMBS Trust Secured Borrowings</link:label>
    <link:label id="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings_documentation_en-US" xlink:label="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance CMBS Trust Secured Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:href="bsprt-20260930.xsd#bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:to="lab_bsprt_ProceedsFromIssuanceCMBSTrustSecuredBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateDomain_01a16142-bad0-7ba1-b0fd-8de1341b6caa_terseLabel_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate [Domain]</link:label>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateDomain_label_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate [Domain]</link:label>
    <link:label id="lab_bsprt_ProfitDistributionHurdleRateDomain_documentation_en-US" xlink:label="lab_bsprt_ProfitDistributionHurdleRateDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Profit Distribution Hurdle Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ProfitDistributionHurdleRateDomain" xlink:href="bsprt-20260930.xsd#bsprt_ProfitDistributionHurdleRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ProfitDistributionHurdleRateDomain" xlink:to="lab_bsprt_ProfitDistributionHurdleRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_019ff14a-1bcb-7b3b-b500-77dd54230bb2_terseLabel_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale</link:label>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_label_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale [Table Text Block]</link:label>
    <link:label id="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Mortgage Loans, Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:to="lab_bsprt_ScheduleOfMortgageLoansHeldForSaleTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019ff14a-1bcb-7518-aa8f-b33bb08f4183_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019ff14a-1bcb-71f8-959a-febbb7974dd0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019ff14a-1bcb-7ba2-9599-85138fe1bb59_netLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanMortgageFairValueDisclosure_019ff14a-1c3c-7815-836a-a88fc6691399_terseLabel_en-US" xlink:label="lab_bsprt_LoanMortgageFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, at fair value</link:label>
    <link:label id="lab_bsprt_LoanMortgageFairValueDisclosure_label_en-US" xlink:label="lab_bsprt_LoanMortgageFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Fair Value Disclosure</link:label>
    <link:label id="lab_bsprt_LoanMortgageFairValueDisclosure_documentation_en-US" xlink:label="lab_bsprt_LoanMortgageFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanMortgageFairValueDisclosure" xlink:href="bsprt-20260930.xsd#bsprt_LoanMortgageFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanMortgageFairValueDisclosure" xlink:to="lab_bsprt_LoanMortgageFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialPortfolioSegmentMember_019ff14a-1bcb-7983-8180-d13030ac31a2_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Portfolio Segment</link:label>
    <link:label id="lab_us-gaap_CommercialPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommercialPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialPortfolioSegmentMember" xlink:to="lab_us-gaap_CommercialPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_019ff14a-1bcb-7b5b-b56b-5cd230c763d1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_01a17ea3-016f-7325-95fb-4631e6c2590b_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt redeemed</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfDebt" xlink:to="lab_us-gaap_RepaymentsOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019ff14a-1bcb-7aa0-a270-0d6c5e4ca4be_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_019ff14a-1c3b-7c09-84d2-a4655f1829df_terseLabel_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc</link:label>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_label_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc [Member]</link:label>
    <link:label id="lab_bsprt_FranklinBSPRealtyTrustIncMember_documentation_en-US" xlink:label="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Franklin BSP Realty Trust, Inc</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FranklinBSPRealtyTrustIncMember" xlink:href="bsprt-20260930.xsd#bsprt_FranklinBSPRealtyTrustIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FranklinBSPRealtyTrustIncMember" xlink:to="lab_bsprt_FranklinBSPRealtyTrustIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_019ff14a-1bcb-7272-9a58-f42d8cf55305_terseLabel_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred financing cost and discount</link:label>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_label_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs And Discount</link:label>
    <link:label id="lab_bsprt_DebtIssuanceCostsAndDiscount_documentation_en-US" xlink:label="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs and Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtIssuanceCostsAndDiscount" xlink:href="bsprt-20260930.xsd#bsprt_DebtIssuanceCostsAndDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtIssuanceCostsAndDiscount" xlink:to="lab_bsprt_DebtIssuanceCostsAndDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019ff14a-1bcb-7b70-9d5a-a5d130f33f0d_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_019ff14a-1b48-7081-af5e-68e0763c9880_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rental income</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLeaseIncome_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLeaseIncome" xlink:to="lab_us-gaap_OperatingLeaseLeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_019ff14a-1bcb-726e-914c-7dbd2da3f9a9_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_019ff14a-1b49-73e9-b4a5-20156e15adf6_terseLabel_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_label_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Originated Mortgage Servicing Rights Revenue</link:label>
    <link:label id="lab_bsprt_OriginatedMortgageServicingRightsRevenue_documentation_en-US" xlink:label="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Originated Mortgage Servicing Rights Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:href="bsprt-20260930.xsd#bsprt_OriginatedMortgageServicingRightsRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:to="lab_bsprt_OriginatedMortgageServicingRightsRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValueOutstanding_019ff14a-1bcb-75a9-a274-a809cfc52e87_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock - at par value</link:label>
    <link:label id="lab_us-gaap_CommonStockValueOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockValueOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValueOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValueOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValueOutstanding" xlink:to="lab_us-gaap_CommonStockValueOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_WeightedAverageMember_019ff14a-1b49-72af-a9d2-d28d798c099f_terseLabel_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average</link:label>
    <link:label id="lab_srt_WeightedAverageMember_label_en-US" xlink:label="lab_srt_WeightedAverageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_WeightedAverageMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_WeightedAverageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_WeightedAverageMember" xlink:to="lab_srt_WeightedAverageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust_019ff14a-1c3b-7bfb-a4ca-072eef2c60bc_verboseLabel_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change in net assets of consolidated VIE, CMBS trust</link:label>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust_019ff14a-1c3b-73a4-a32c-099deb6f0e24_totalLabel_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Change in net assets of consolidated variable interest entity</link:label>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust_label_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change In Net Assets Of Variable Interest Entity, CMBS Trust</link:label>
    <link:label id="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust_documentation_en-US" xlink:label="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Change In Net Assets Of Variable Interest Entity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:href="bsprt-20260930.xsd#bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:to="lab_bsprt_ChangeInNetAssetsOfVariableInterestEntityCMBSTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019ff14a-1bcb-71dc-b297-a220a5374dd7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019ff14a-1bcb-7489-b981-5b8c2816e1c3_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_019ff14a-1c3b-71e2-8f5e-5926c41d746f_terseLabel_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior Note II</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_label_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note II, Maturing December 2035 [Member]</link:label>
    <link:label id="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member_documentation_en-US" xlink:label="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Junior Subordinated Note II, Maturing December 2035</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:href="bsprt-20260930.xsd#bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:to="lab_bsprt_JuniorSubordinatedNoteIIMaturingDecember2035Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireNotesReceivable_019ff14a-1bcb-7170-88a9-5ba70c1f0342_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate principal balance</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireNotesReceivable_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Notes Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireNotesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireNotesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireNotesReceivable" xlink:to="lab_us-gaap_PaymentsToAcquireNotesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_019ff14a-1bcb-71b2-b309-04fd45b5e490_totalLabel_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) applicable to common stock, diluted</link:label>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_label_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted, Including Undistributed Earnings (Loss) Allocated to Participating Securities</link:label>
    <link:label id="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities_documentation_en-US" xlink:label="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted, Including Undistributed Earnings (Loss) Allocated to Participating Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:href="bsprt-20260930.xsd#bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:to="lab_bsprt_NetIncomeLossAvailableToCommonStockholdersDilutedIncludingUndistributedEarningsLossAllocatedToParticipatingSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgingPurposeDomain_019ff14a-1bcb-789b-8d08-a39195133cc8_terseLabel_en-US" xlink:label="lab_us-gaap_PledgingPurposeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgingPurposeDomain_label_en-US" xlink:label="lab_us-gaap_PledgingPurposeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledging Purpose [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgingPurposeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgingPurposeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgingPurposeDomain" xlink:to="lab_us-gaap_PledgingPurposeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_019ff14a-1bcb-7653-8887-587a46f74747_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019ff14a-1aa9-7607-b538-28ceeaee1862_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable_019ff14a-1c3b-72dd-a413-9e26378b5cd5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Banking Regulation, Mortgage Banking, Capital Requirement [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Mortgage Banking, Capital Requirement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable" xlink:to="lab_us-gaap_ScheduleOfComplianceWithRegulatoryCapitalRequirementsForMortgageCompaniesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019ff14a-1c3c-7392-958f-5d2f188327ed_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on other real estate investments</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestments" xlink:to="lab_us-gaap_GainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_019ff14a-1b48-7a07-8c20-3a4c8eb64075_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchases Of Pledged Investment Securities</link:label>
    <link:label id="lab_bsprt_PurchasesOfPledgedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchases Of Pledged Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:href="bsprt-20260930.xsd#bsprt_PurchasesOfPledgedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:to="lab_bsprt_PurchasesOfPledgedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019ff14a-1b49-79e1-b4a9-f19b9fd14d9c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_019ff14a-1aa9-7ed1-b7e7-dac07ba56b9d_negatedLabel_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Operating expenses</link:label>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_label_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses, Adjusted</link:label>
    <link:label id="lab_bsprt_OperatingExpensesAdjusted_documentation_en-US" xlink:label="lab_bsprt_OperatingExpensesAdjusted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Expenses, Adjusted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_OperatingExpensesAdjusted" xlink:href="bsprt-20260930.xsd#bsprt_OperatingExpensesAdjusted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_OperatingExpensesAdjusted" xlink:to="lab_bsprt_OperatingExpensesAdjusted" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_019ff14a-1aa9-77b1-acd4-76fd8e399aad_terseLabel_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate (percentage)</link:label>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_label_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Discount Rate</link:label>
    <link:label id="lab_bsprt_FairValueInputsDiscountRate_documentation_en-US" xlink:label="lab_bsprt_FairValueInputsDiscountRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueInputsDiscountRate" xlink:href="bsprt-20260930.xsd#bsprt_FairValueInputsDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FairValueInputsDiscountRate" xlink:to="lab_bsprt_FairValueInputsDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember_019ff14a-1bcb-7969-911d-54fc537293a8_terseLabel_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Combined Specific</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember_label_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Combined Specific [Member]</link:label>
    <link:label id="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember_documentation_en-US" xlink:label="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Allowance for Credit Loss, Combined Specific</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:href="bsprt-20260930.xsd#bsprt_AllowanceForCreditLossCombinedSpecificMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:to="lab_bsprt_AllowanceForCreditLossCombinedSpecificMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnitsRedeemed_01a160e8-2856-7695-9dc0-e549fb233233_verboseLabel_en-US" xlink:label="lab_bsprt_UnitsRedeemed" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">OP Units redeemed for common stock</link:label>
    <link:label id="lab_bsprt_UnitsRedeemed_label_en-US" xlink:label="lab_bsprt_UnitsRedeemed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Units Redeemed</link:label>
    <link:label id="lab_bsprt_UnitsRedeemed_documentation_en-US" xlink:label="lab_bsprt_UnitsRedeemed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Units Redeemed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnitsRedeemed" xlink:href="bsprt-20260930.xsd#bsprt_UnitsRedeemed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnitsRedeemed" xlink:to="lab_bsprt_UnitsRedeemed" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_019ff14a-1aa9-7b5a-bf90-ebf3973cdf30_terseLabel_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities, LLC</link:label>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_label_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities LLC [Member]</link:label>
    <link:label id="lab_bsprt_WellsFargoSecuritiesLLCMember_documentation_en-US" xlink:label="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Wells Fargo Securities LLC [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_WellsFargoSecuritiesLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_WellsFargoSecuritiesLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_WellsFargoSecuritiesLLCMember" xlink:to="lab_bsprt_WellsFargoSecuritiesLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_HuntersvilleNorthCarolinaMember_019ff14a-1c3c-7495-be54-c58a6a2cf567_terseLabel_en-US" xlink:label="lab_bsprt_HuntersvilleNorthCarolinaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Huntersville, NC</link:label>
    <link:label id="lab_bsprt_HuntersvilleNorthCarolinaMember_label_en-US" xlink:label="lab_bsprt_HuntersvilleNorthCarolinaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Huntersville, North Carolina [Member]</link:label>
    <link:label id="lab_bsprt_HuntersvilleNorthCarolinaMember_documentation_en-US" xlink:label="lab_bsprt_HuntersvilleNorthCarolinaMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Huntersville, North Carolina</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_HuntersvilleNorthCarolinaMember" xlink:href="bsprt-20260930.xsd#bsprt_HuntersvilleNorthCarolinaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_HuntersvilleNorthCarolinaMember" xlink:to="lab_bsprt_HuntersvilleNorthCarolinaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019ff14a-1c3b-7c72-94d1-75a0980d57f1_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_01a152e6-2e2a-7656-ab60-4a93f034e1a5_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of OP Units to common stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_019ff14a-1aa9-78f3-8db2-df98b9172903_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk</link:label>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeographicConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeographicConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeographicConcentrationRiskMember" xlink:to="lab_us-gaap_GeographicConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019ff14a-1b49-733e-8c08-c216bfaabec2_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_019ff14a-1b48-755b-ab75-ca7aa73116ea_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_019ff14a-1b48-7cd8-95d8-ed87b4fac27e_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LucidPrimeFundMember_019ff14a-1aa8-7dc1-b743-e8181e186079_terseLabel_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund</link:label>
    <link:label id="lab_bsprt_LucidPrimeFundMember_label_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund [Member]</link:label>
    <link:label id="lab_bsprt_LucidPrimeFundMember_documentation_en-US" xlink:label="lab_bsprt_LucidPrimeFundMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lucid Prime Fund</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LucidPrimeFundMember" xlink:href="bsprt-20260930.xsd#bsprt_LucidPrimeFundMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LucidPrimeFundMember" xlink:to="lab_bsprt_LucidPrimeFundMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualRollForward_019ff14a-1aa9-7dfa-8127-08da62cf6f1c_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualRollForward_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualRollForward" xlink:to="lab_us-gaap_LossContingencyAccrualRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019ff14a-1c3c-7060-924b-7edc92307d41_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_019ff14a-1c3b-73bf-8352-6fc5cc1cf79c_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_019ff14a-1bcb-7645-b8d1-a69fd1959eb1_terseLabel_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum annual subordinated performance fee payable percent of total return</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_label_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee Maximum</link:label>
    <link:label id="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum_documentation_en-US" xlink:label="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction Subordinated Participation In Asset Sale Fee Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:href="bsprt-20260930.xsd#bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:to="lab_bsprt_RelatedPartyTransactionSubordinatedParticipationInAssetSaleFeeMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_InvestmentRating1Member_019ff14a-1b48-79d8-82f1-a9bdc54a0745_terseLabel_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1</link:label>
    <link:label id="lab_bsprt_InvestmentRating1Member_label_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Rating 1 [Member]</link:label>
    <link:label id="lab_bsprt_InvestmentRating1Member_documentation_en-US" xlink:label="lab_bsprt_InvestmentRating1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Rating 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_InvestmentRating1Member" xlink:href="bsprt-20260930.xsd#bsprt_InvestmentRating1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_InvestmentRating1Member" xlink:to="lab_bsprt_InvestmentRating1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract_019ff14a-1b48-7672-b95a-fcdf936e4714_terseLabel_en-US" xlink:label="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock:</link:label>
    <link:label id="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract_label_en-US" xlink:label="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Features of Convertible Preferred Stock [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FeaturesOfConvertiblePreferredStockAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:to="lab_us-gaap_FeaturesOfConvertiblePreferredStockAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_019ff14a-1b49-7036-8019-e99089d5334d_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_019ff14a-1bcb-7e57-9938-de9d50116d6e_terseLabel_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture, Fixtures and Equipment</link:label>
    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_label_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture Fixtures and Equipment [Member]</link:label>
    <link:label id="lab_bsprt_FurnitureFixturesandEquipmentMember_documentation_en-US" xlink:label="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Furniture Fixtures and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FurnitureFixturesandEquipmentMember" xlink:href="bsprt-20260930.xsd#bsprt_FurnitureFixturesandEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FurnitureFixturesandEquipmentMember" xlink:to="lab_bsprt_FurnitureFixturesandEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_019ff14a-1b49-7a49-b965-ba8aad767b49_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Credit Quality Indicator [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_019ff14a-1b49-7d02-afb4-ee7b49b58678_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_019ff14a-1b49-7e0b-9d32-5329ce4d1d33_verboseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_019ff14a-1b49-7d8f-8b32-219b4ce833dc_netLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Commercial mortgage loans, held for sale, measured at fair value - Non-Agency</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MortgagesHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_019ff14a-1c3c-7ab8-a50b-deaac080f111_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets and liabilities measured at fair value, net</link:label>
    <link:label id="lab_us-gaap_FairValueNetAssetLiability_label_en-US" xlink:label="lab_us-gaap_FairValueNetAssetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Net Asset (Liability)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueNetAssetLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueNetAssetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueNetAssetLiability" xlink:to="lab_us-gaap_FairValueNetAssetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019ff14a-1bcb-7583-aa2d-54239f190d9a_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs_019ff14a-1bcb-7d2c-a51a-61b49dd80c9c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR amortization</link:label>
    <link:label id="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs_label_en-US" xlink:label="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Mortgage Servicing Rights (MSRs)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfMortgageServicingRightsMSRs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:to="lab_us-gaap_AmortizationOfMortgageServicingRightsMSRs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_019ff14a-1aa9-7ced-a203-f5e03922c58d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of positions in unrealized loss position 12 months or longer</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019ff14a-1bcb-7984-b0b1-dcfee62c29f4_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_019ff14a-1c3b-71e8-a9d5-efc4d080ad3c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts Offset on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, Liability Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:to="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019ff14a-1bcb-7401-916f-8dc8cb62f40a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FreddieMacMember_019ff14a-1c3c-7414-a52f-061bcc12a784_terseLabel_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:label id="lab_bsprt_FreddieMacMember_label_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Freddie Mac [Member]</link:label>
    <link:label id="lab_bsprt_FreddieMacMember_documentation_en-US" xlink:label="lab_bsprt_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FreddieMacMember" xlink:href="bsprt-20260930.xsd#bsprt_FreddieMacMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FreddieMacMember" xlink:to="lab_bsprt_FreddieMacMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CMBSBondsIssuedVIECMBSTrust_019ff14a-1c3c-75c9-abbc-6240db279081_terseLabel_en-US" xlink:label="lab_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS bonds issued via consolidated VIE CMBS trust</link:label>
    <link:label id="lab_bsprt_CMBSBondsIssuedVIECMBSTrust_label_en-US" xlink:label="lab_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CMBS Bonds Issued, VIE CMBS Trust</link:label>
    <link:label id="lab_bsprt_CMBSBondsIssuedVIECMBSTrust_documentation_en-US" xlink:label="lab_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CMBS Bonds Issued, VIE CMBS Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:href="bsprt-20260930.xsd#bsprt_CMBSBondsIssuedVIECMBSTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:to="lab_bsprt_CMBSBondsIssuedVIECMBSTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SfpLocationActivityCapitalizationAxis_019ff14a-1b49-7a68-afe8-8445de4a91a6_terseLabel_en-US" xlink:label="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Activity, Capitalization [Axis]</link:label>
    <link:label id="lab_us-gaap_SfpLocationActivityCapitalizationAxis_label_en-US" xlink:label="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Activity, Capitalization [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SfpLocationActivityCapitalizationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:to="lab_us-gaap_SfpLocationActivityCapitalizationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_019ff14a-1bcb-7485-ae41-ab0bd5ec6412_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - real estate securities</link:label>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_label_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Securities [Member]</link:label>
    <link:label id="lab_bsprt_RealEstateSecuritiesMember_documentation_en-US" xlink:label="lab_bsprt_RealEstateSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateSecuritiesMember" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateSecuritiesMember" xlink:to="lab_bsprt_RealEstateSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductInformationLineItems_019ff14a-1b49-7325-995d-243bcd20d302_terseLabel_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_ProductInformationLineItems_label_en-US" xlink:label="lab_us-gaap_ProductInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProductInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductInformationLineItems" xlink:to="lab_us-gaap_ProductInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_019ff14a-1bcb-7f40-a5de-1b17ba9e8289_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill acquired during the period</link:label>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_label_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAcquiredDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:to="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_019ff14a-1b49-75c2-bc5b-f474ef238823_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VariousLocationsMember_019ff14a-1b49-7707-a380-d7d0bf610c1e_terseLabel_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Various</link:label>
    <link:label id="lab_bsprt_VariousLocationsMember_label_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Various Locations [Member]</link:label>
    <link:label id="lab_bsprt_VariousLocationsMember_documentation_en-US" xlink:label="lab_bsprt_VariousLocationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Various Geographic Locations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VariousLocationsMember" xlink:href="bsprt-20260930.xsd#bsprt_VariousLocationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VariousLocationsMember" xlink:to="lab_bsprt_VariousLocationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_019ff14a-1bcb-7e22-8d13-58085b14fc18_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, gross</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Gross</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentGross_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedHeldForInvestmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:to="lab_bsprt_RealEstateOwnedHeldForInvestmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019ff14a-1c3b-7484-bc9d-90ea501f8314_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_019ff14a-1aa9-77d8-b03a-c95d7cd51f97_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Investment Securities</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredRestrictedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019ff14a-1b48-7b75-b578-85e90d63ddd7_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income/(Loss) for Real Estate Securities, Available for Sale, Measured at Fair Value</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:to="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_019ff14a-1c3b-794c-b76a-c35aa7f424b1_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
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    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_019ff14a-1b48-7cea-a2a3-e69c6d2ab584_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Derivative Assets</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Derivative Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_019ff14a-1c3c-746b-ae24-fcc4e4350d83_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurements, Recurring and Nonrecurring, Valuation Techniques</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_019ff14a-1c3b-7bd0-a903-0b8536128138_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net unrealized gain/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_019ff14a-1b48-72c8-b88b-8e9f51924460_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019ff14a-1b49-7b8f-9aca-f6834cc14386_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019ff14a-1aa9-7151-bdb4-29c627d363a8_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash (used in)/provided by financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_019ff14a-1b49-7d50-b69a-15d8fd9c29ad_negatedLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Shares canceled for tax withholding on vested equity rewards</link:label>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Decrease for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstate_019ff14a-1bcb-7634-bd7c-1060f9e1a775_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire property</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstate_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireRealEstate" xlink:to="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_019ff14a-1b48-70a3-9076-03eb834923fe_terseLabel_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for loans eligible for repurchase</link:label>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_label_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Repurchase Option, Liabilities</link:label>
    <link:label id="lab_bsprt_LoanRepurchaseOptionLiabilities_documentation_en-US" xlink:label="lab_bsprt_LoanRepurchaseOptionLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Repurchase Option, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanRepurchaseOptionLiabilities" xlink:href="bsprt-20260930.xsd#bsprt_LoanRepurchaseOptionLiabilities"/>
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    <link:label id="lab_bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue_019ff14a-1bcb-7ba9-8717-3bf3ac865f00_negatedLabel_en-US" xlink:label="lab_bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized (gain)/loss on sale of commercial mortgage loans, held for sale, measured at fair value</link:label>
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    <link:label id="lab_bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue_documentation_en-US" xlink:label="lab_bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US"></link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue" xlink:href="bsprt-20260930.xsd#bsprt_RealizedAndUnrealizedGainLossOnSaleOfMortgageLoansHeldForSaleMeasuredAtFairValue"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_019ff14a-1bcb-7051-b54a-cf9a1cd532f8_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:to="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnsecuredSeniorNotesIMember_019ff14a-1bcb-7a9f-8263-46a4f23489b8_terseLabel_en-US" xlink:label="lab_bsprt_UnsecuredSeniorNotesIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Senior Notes I</link:label>
    <link:label id="lab_bsprt_UnsecuredSeniorNotesIMember_label_en-US" xlink:label="lab_bsprt_UnsecuredSeniorNotesIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Senior Notes I [Member]</link:label>
    <link:label id="lab_bsprt_UnsecuredSeniorNotesIMember_documentation_en-US" xlink:label="lab_bsprt_UnsecuredSeniorNotesIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Senior Notes I</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnsecuredSeniorNotesIMember" xlink:href="bsprt-20260930.xsd#bsprt_UnsecuredSeniorNotesIMember"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_019ff14a-1aa9-7a5d-ba5a-887f17144c25_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Business Combination, Pro Forma Information</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionProFormaInformationTextBlock"/>
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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019ff14a-1bcb-76c0-a698-72415a22ae61_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash (used in)/provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019ff14a-1bcb-7c35-bbe4-e724cd29f5bb_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_019ff14a-1c3b-70ca-b5d1-8f0b4a35aaf0_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ServicingFeesRevenue_019ff14a-1bcb-726a-aa6d-a10cf840151f_terseLabel_en-US" xlink:label="lab_bsprt_ServicingFeesRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fee income</link:label>
    <link:label id="lab_bsprt_ServicingFeesRevenue_label_en-US" xlink:label="lab_bsprt_ServicingFeesRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Fees Revenue</link:label>
    <link:label id="lab_bsprt_ServicingFeesRevenue_documentation_en-US" xlink:label="lab_bsprt_ServicingFeesRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Servicing Fees Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ServicingFeesRevenue" xlink:href="bsprt-20260930.xsd#bsprt_ServicingFeesRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ServicingFeesRevenue" xlink:to="lab_bsprt_ServicingFeesRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_019ff14a-1bcb-747a-bbe2-3d50a568e2de_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year five, original in prior fiscal year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Five, Originated, Four Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFiveOriginatedFourYearsBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_019ff14a-1bcb-7128-ad5c-470d967a569a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, measured at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_019ff14a-1b49-78b0-86fc-2f8a159710d7_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAbstract_019ff14a-1b49-7f18-b566-b0eb426ca71f_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:label id="lab_us-gaap_OffsettingAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAbstract" xlink:to="lab_us-gaap_OffsettingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_019ff14a-1aa9-7d7f-add6-64e0c822199c_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill &amp; Other Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset and Goodwill [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale_019ff14a-1bcb-75ed-9d13-7118b581f915_terseLabel_en-US" xlink:label="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans transferred from commercial mortgage loans, held for investment to real estate owned, held for sale</link:label>
    <link:label id="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale_label_en-US" xlink:label="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Transferred To Real Estate Owned, Held-for-Sale</link:label>
    <link:label id="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale_documentation_en-US" xlink:label="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Transferred To Real Estate Owned, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:href="bsprt-20260930.xsd#bsprt_LoansTransferredToRealEstateOwnedHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:to="lab_bsprt_LoansTransferredToRealEstateOwnedHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019ff14a-1bcb-7330-bf83-75f7649a39d5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (income)/loss attributed to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019ff14a-1b49-7ba7-82b4-ce1fc94a27ec_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_019ff14a-1aa9-763e-9ce3-723fbbabe3ed_terseLabel_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury note futures</link:label>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_label_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Note Futures [Member]</link:label>
    <link:label id="lab_bsprt_TreasuryNoteFuturesMember_documentation_en-US" xlink:label="lab_bsprt_TreasuryNoteFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Note Futures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_TreasuryNoteFuturesMember" xlink:href="bsprt-20260930.xsd#bsprt_TreasuryNoteFuturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_TreasuryNoteFuturesMember" xlink:to="lab_bsprt_TreasuryNoteFuturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_019ff14a-1b48-723c-b15d-2fd3d11e495a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred E</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_019ff14a-1aa8-7982-8488-d54ce65027a3_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average discount rate</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019ff14a-1b49-7feb-be5a-c6d2e1b5f21b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019ff14a-1b49-756e-aea3-09d6da662c24_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions, by Related Party [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_019ff14a-1b49-7473-9046-6e48d65c26c9_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Revenue since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:to="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_019ff14a-1bcb-706f-bdee-fdca5bfb3fba_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lease, Cost</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_March2022MultifamilyMember_01a15306-aae2-7422-91bb-7aec9cbc506a_terseLabel_en-US" xlink:label="lab_bsprt_March2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">March 2022 Multifamily</link:label>
    <link:label id="lab_bsprt_March2022MultifamilyMember_label_en-US" xlink:label="lab_bsprt_March2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">March 2022 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_March2022MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_March2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">March 2022 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_March2022MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_March2022MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_March2022MultifamilyMember" xlink:to="lab_bsprt_March2022MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_019ff14a-1aa8-70a6-acee-f469a7ddaaea_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_019ff14a-1bcb-771e-afba-d8188ae9606f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of securities in an unrealized loss position, less than 12 months</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019ff14a-1bcb-7195-9198-84f18d6b63a7_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanHeldInPortfolioOutstandingAmount_019ff14a-1c3c-79d6-8a16-3803ac21d0c0_terseLabel_en-US" xlink:label="lab_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding principal balance</link:label>
    <link:label id="lab_bsprt_LoanHeldInPortfolioOutstandingAmount_label_en-US" xlink:label="lab_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-In-Portfolio, Outstanding Amount</link:label>
    <link:label id="lab_bsprt_LoanHeldInPortfolioOutstandingAmount_documentation_en-US" xlink:label="lab_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan, Held-In-Portfolio, Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:href="bsprt-20260930.xsd#bsprt_LoanHeldInPortfolioOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:to="lab_bsprt_LoanHeldInPortfolioOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019ff14a-1bcb-7a82-82a3-1dd8ee5e7382_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019ff14a-1bcb-74f8-a2c6-4aef750f9e9d_negatedLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019ff14a-1bcb-723a-a638-5dbed294ff59_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Provision/(benefit) for credit losses</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019ff14a-1bcb-7c75-9b1e-101430119956_netLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Provision/(Benefit)</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_019ff14a-1b49-7e49-a6b9-88507b5ceb47_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SpecificReserveMember_019ff14a-1bcb-7c0c-8833-d1cb8ac8c974_terseLabel_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Specific Reserve</link:label>
    <link:label id="lab_bsprt_SpecificReserveMember_label_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Specific Reserve [Member]</link:label>
    <link:label id="lab_bsprt_SpecificReserveMember_documentation_en-US" xlink:label="lab_bsprt_SpecificReserveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Specific Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SpecificReserveMember" xlink:href="bsprt-20260930.xsd#bsprt_SpecificReserveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SpecificReserveMember" xlink:to="lab_bsprt_SpecificReserveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward_019ff14a-1aa9-76c3-8c0a-e185dfe1bb64_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Asset [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Amortized Cost, Balance [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward" xlink:to="lab_us-gaap_ServicingAssetAtAmortizedValueBalanceRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019ff14a-1bcb-7754-907a-fa7ca5f38600_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common stock repurchases (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019ff14a-1bcb-78f3-a5e6-a5ea0532cf05_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember_019ff14a-1bcb-75d6-a387-696f966ab4bf_terseLabel_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Investment</link:label>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember_label_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Investment [Member]</link:label>
    <link:label id="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember_documentation_en-US" xlink:label="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Mortgage Receivable, Held-For-Investment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:href="bsprt-20260930.xsd#bsprt_CommercialMortgageReceivableHeldForInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:to="lab_bsprt_CommercialMortgageReceivableHeldForInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_019ff14a-1b48-7216-8db4-51fd244d74da_totalLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_019ff14a-1bcb-7a9a-9c7d-d59d924cf1d3_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividends declared (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019ff14a-1b49-7f04-b9e4-3b25104ca6ca_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OfficeBuildingMember_019ff14a-1b49-73d2-b18d-eb47bbfe5540_terseLabel_en-US" xlink:label="lab_srt_OfficeBuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Office</link:label>
    <link:label id="lab_srt_OfficeBuildingMember_label_en-US" xlink:label="lab_srt_OfficeBuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Office Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OfficeBuildingMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OfficeBuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OfficeBuildingMember" xlink:to="lab_srt_OfficeBuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AgencyMember_019ff14a-1b49-7df8-a518-22497f70dd3e_terseLabel_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency Business</link:label>
    <link:label id="lab_bsprt_AgencyMember_label_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency [Member]</link:label>
    <link:label id="lab_bsprt_AgencyMember_documentation_en-US" xlink:label="lab_bsprt_AgencyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AgencyMember" xlink:href="bsprt-20260930.xsd#bsprt_AgencyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AgencyMember" xlink:to="lab_bsprt_AgencyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_019ff14a-1bcb-7d16-b9cc-f139399dd8ea_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing revenue, net</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractuallySpecifiedServicingFeesAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:to="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_019ff14a-1bcb-774e-a459-dfcae88b5900_terseLabel_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on other real estate investments</link:label>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_label_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Other Real Estate Investments</link:label>
    <link:label id="lab_bsprt_GainLossOnOtherRealEstateInvestments_documentation_en-US" xlink:label="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Other Real Estate Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GainLossOnOtherRealEstateInvestments" xlink:href="bsprt-20260930.xsd#bsprt_GainLossOnOtherRealEstateInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GainLossOnOtherRealEstateInvestments" xlink:to="lab_bsprt_GainLossOnOtherRealEstateInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareDeclared_019ff14a-1b48-7617-a7ae-2c0844174d87_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends declared (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividends Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockDividendsPerShareDeclared"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsPerShareDeclared" xlink:to="lab_us-gaap_PreferredStockDividendsPerShareDeclared" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoanCommitmentsMember_019ff14a-1b49-74f7-9978-57e8304c6ff8_terseLabel_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward sale commitments</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsMember_label_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan commitments [Member]</link:label>
    <link:label id="lab_bsprt_LoanCommitmentsMember_documentation_en-US" xlink:label="lab_bsprt_LoanCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoanCommitmentsMember" xlink:href="bsprt-20260930.xsd#bsprt_LoanCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoanCommitmentsMember" xlink:to="lab_bsprt_LoanCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_019ff14a-1bcb-78ef-bc13-eea85c60a9f7_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_019ff14a-1c3b-7628-b05b-09bd9a757466_terseLabel_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_label_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Number of Bonds</link:label>
    <link:label id="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds_documentation_en-US" xlink:label="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Number of Bonds</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:href="bsprt-20260930.xsd#bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:to="lab_bsprt_DebtSecuritiesAvailableForSaleNumberOfBonds" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019ff14a-1bcb-7a8f-9eeb-1cfded9fdbf8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Collateralized Loan Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019ff14a-1bcb-739c-8ea1-885bd057d495_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossSharingObligationsPercent_019ff14a-1b49-77ec-9746-a9d32ff78804_terseLabel_en-US" xlink:label="lab_bsprt_LossSharingObligationsPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss-sharing obligations, percent</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsPercent_label_en-US" xlink:label="lab_bsprt_LossSharingObligationsPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss-Sharing Obligations, Percent</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsPercent_documentation_en-US" xlink:label="lab_bsprt_LossSharingObligationsPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss-Sharing Obligations, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsPercent" xlink:href="bsprt-20260930.xsd#bsprt_LossSharingObligationsPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossSharingObligationsPercent" xlink:to="lab_bsprt_LossSharingObligationsPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GardenaJVMember_019ff14a-1c3b-7ff9-9036-0cc7b908a70e_terseLabel_en-US" xlink:label="lab_bsprt_GardenaJVMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gardena JV</link:label>
    <link:label id="lab_bsprt_GardenaJVMember_label_en-US" xlink:label="lab_bsprt_GardenaJVMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gardena JV [Member]</link:label>
    <link:label id="lab_bsprt_GardenaJVMember_documentation_en-US" xlink:label="lab_bsprt_GardenaJVMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gardena JV</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GardenaJVMember" xlink:href="bsprt-20260930.xsd#bsprt_GardenaJVMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GardenaJVMember" xlink:to="lab_bsprt_GardenaJVMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019ff14a-1bcb-77ff-9ca2-ab964f516870_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019ff14a-1b49-7259-af70-c4d4ca324776_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_February2026ReauthorizationMember_019ff14a-1c3c-7296-a463-3b3400d17c94_terseLabel_en-US" xlink:label="lab_bsprt_February2026ReauthorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">February 2026 Reauthorization</link:label>
    <link:label id="lab_bsprt_February2026ReauthorizationMember_label_en-US" xlink:label="lab_bsprt_February2026ReauthorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">February 2026 Reauthorization [Member]</link:label>
    <link:label id="lab_bsprt_February2026ReauthorizationMember_documentation_en-US" xlink:label="lab_bsprt_February2026ReauthorizationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">February 2026 Reauthorization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_February2026ReauthorizationMember" xlink:href="bsprt-20260930.xsd#bsprt_February2026ReauthorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_February2026ReauthorizationMember" xlink:to="lab_bsprt_February2026ReauthorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_019ff14a-1b49-75a3-be01-4ecacbcaaf73_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of repurchase agreements and revolving credit facilities - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_label_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:label id="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable_documentation_en-US" xlink:label="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments From Securities Purchased Under Agreements To Resell, Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:href="bsprt-20260930.xsd#bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:to="lab_bsprt_PaymentsFromSecuritiesPurchasedUnderAgreementsToResellLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019ff14a-1bcb-7ccd-8a2d-d38a1dd5d750_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_019ff14a-1b49-78d7-8870-a7e98a05b432_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019ff14a-1b49-7f07-9299-07a952fe35ed_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net (income)/loss attributable to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019ff14a-1b49-7b76-bc53-43f6bf3a0e7d_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss) attributable to non-controlling interest</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction_01a164c9-5557-719f-a3df-ead90e6f5e90_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, gross amounts not offset on the balance sheet, Financial Instruments</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Deduction of Financial Instrument Not Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToResellNotOffsetPolicyElectionDeduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_01a152e2-d2ef-7d1b-8af1-43744022942d_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of OP units to common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax_019ff14a-1b49-7c93-bbe9-cf33be9127cb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification adjustment for amounts included in net income/(loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Reclassification Adjustment from AOCI for Sale of Securities, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019ff14a-1b49-7aee-99a2-8bb528dec20e_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019ff14a-1b48-71fe-9cca-fe3d65d9ba06_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income/(loss) attributable to Franklin BSP Realty Trust, Inc.</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_019ff14a-1aa9-7bc9-9d0d-b3550d97c8fa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares canceled for tax withholding on vested equity rewards (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_019ff14a-1aa9-7fbf-9114-8a91557303c6_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average useful economic useful life</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired, Weighted-Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus_019ff14a-1c3c-7923-bfe1-c52602312b90_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of nonperforming loans on cost recovery status</link:label>
    <link:label id="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus_label_en-US" xlink:label="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Nonperforming Loans On Cost Recovery Status</link:label>
    <link:label id="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus_documentation_en-US" xlink:label="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Nonperforming Loans On Cost Recovery Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:href="bsprt-20260930.xsd#bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:to="lab_bsprt_NumberOfNonperformingLoansOnCostRecoveryStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GSEMember_019ff14a-1bcb-76ab-a8ea-728f53aad0ee_terseLabel_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CML, HFS, measured at fair value - Agency</link:label>
    <link:label id="lab_bsprt_GSEMember_label_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GSE [Member]</link:label>
    <link:label id="lab_bsprt_GSEMember_documentation_en-US" xlink:label="lab_bsprt_GSEMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GSE</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GSEMember" xlink:href="bsprt-20260930.xsd#bsprt_GSEMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GSEMember" xlink:to="lab_bsprt_GSEMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_019ff14a-1b48-76f1-8b6f-39f129413117_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_label_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income (Expense), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeExpenseNet" xlink:to="lab_us-gaap_InterestIncomeExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_01a164c4-2efd-7786-90cb-233c239f8d54_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amount of Assets Presented on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod_019ff14a-1bcb-7201-b478-70aa698a2d3e_terseLabel_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mandatory conversion date, extension period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod_label_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock Converted To Common Stock, Mandatory Conversion Date Extension Period</link:label>
    <link:label id="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod_documentation_en-US" xlink:label="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Preferred Stock Converted To Common Stock, Mandatory Conversion Date Extension Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:href="bsprt-20260930.xsd#bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:to="lab_bsprt_ConversionOfStockPreferredStockConvertedToCommonStockMandatoryConversionDateExtensionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019ff14a-1b49-7a78-950e-3bd9173ce38c_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019ff14a-1bcb-7025-8e19-5d86dd30f03d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019ff14a-1bcb-7e7a-9048-8ab64976871b_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019ff14a-1bcb-76e2-9e0a-c7c995e2014d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized gain/(loss) on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019ff14a-1b49-7ae2-ab91-e722ec0b3ec8_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_019ff14a-1aa9-7bd8-8e8b-59f71ba603fc_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019ff14a-1bcb-76f9-a4cb-80ce514343e8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019ff14a-1bcb-7963-8568-00677955ef95_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_HospitalityMember_019ff14a-1bcb-72de-be39-c539be26710a_terseLabel_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hospitality</link:label>
    <link:label id="lab_bsprt_HospitalityMember_label_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hospitality [Member]</link:label>
    <link:label id="lab_bsprt_HospitalityMember_documentation_en-US" xlink:label="lab_bsprt_HospitalityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hospitality</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_HospitalityMember" xlink:href="bsprt-20260930.xsd#bsprt_HospitalityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_HospitalityMember" xlink:to="lab_bsprt_HospitalityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PledgedStatusDomain_019ff14a-1bcb-72df-bbc3-1f08f86ef819_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PledgedStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusDomain" xlink:to="lab_us-gaap_PledgedStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019ff14a-1bcb-77c2-8575-8d8d7b847f54_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_019ff14a-1c3b-7c7c-9c4e-77b52499bb08_terseLabel_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility</link:label>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_AtlasRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_AtlasRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Atlas Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AtlasRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_AtlasRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AtlasRepoFacilityMember" xlink:to="lab_bsprt_AtlasRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019ff14a-1b49-789c-be34-ea5b4bddde43_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract_019ff14a-1b49-75fe-bc82-a4950b0422c1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amounts related to available for sale real estate securities:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment and Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeAvailableForSaleSecuritiesAdjustmentNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019ff14a-1b48-7cb6-8766-db4873c12ff4_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_019ff14a-1b48-7604-a301-be649af492cb_terseLabel_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company holds common units, membership interest, rate</link:label>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_label_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Holds Common Units, Membership Interest, Rate</link:label>
    <link:label id="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate_documentation_en-US" xlink:label="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Company Holds Common Units, Membership Interest, Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:href="bsprt-20260930.xsd#bsprt_CompanyHoldsCommonUnitsMembershipInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:to="lab_bsprt_CompanyHoldsCommonUnitsMembershipInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_019ff14a-1bcb-767f-b3e2-6b95e3e38402_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan repurchase option asset</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Loan Repurchase Option Asset</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Loan Repurchase Option Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredLoanRepurchaseOptionAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_019ff14a-1bcb-77e4-9b0d-1a245663ad89_terseLabel_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MSR impairment and amortization</link:label>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_label_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment And Amortization Of Mortgage Servicing Rights MSR</link:label>
    <link:label id="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR_documentation_en-US" xlink:label="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment And Amortization Of Mortgage Servicing Rights MSR</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:href="bsprt-20260930.xsd#bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:to="lab_bsprt_ImpairmentAndAmortizationOfMortgageServicingRightsMSR" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019ff14a-1b48-7279-94ca-9fbe721059ce_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019ff14a-1b48-7579-b0f3-8d5ca1e1e6d2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND STOCKHOLDERS' EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_019ff14a-1bcb-7f0b-b24e-ab92887c162b_terseLabel_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for loan repayment</link:label>
    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_label_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables For Loan Repayment</link:label>
    <link:label id="lab_bsprt_ReceivablesForLoanRepayment_documentation_en-US" xlink:label="lab_bsprt_ReceivablesForLoanRepayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivables For Loan Repayment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_ReceivablesForLoanRepayment" xlink:href="bsprt-20260930.xsd#bsprt_ReceivablesForLoanRepayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_ReceivablesForLoanRepayment" xlink:to="lab_bsprt_ReceivablesForLoanRepayment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_019ff14a-1bcb-7649-bdc2-e6a616c193a7_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedFourYears" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_019ff14a-1bcb-78f6-9d60-22a22466db0c_terseLabel_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of note-on-note financings</link:label>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_label_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Financing Agreements</link:label>
    <link:label id="lab_bsprt_NumberOfFinancingAgreements_documentation_en-US" xlink:label="lab_bsprt_NumberOfFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Financing Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NumberOfFinancingAgreements" xlink:href="bsprt-20260930.xsd#bsprt_NumberOfFinancingAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NumberOfFinancingAgreements" xlink:to="lab_bsprt_NumberOfFinancingAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_019ff14a-1b49-7b4f-a8ab-49413450c4dc_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain/(loss) on sales, including fee-based services, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnSalesOfLoansNet_label_en-US" xlink:label="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sales of Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSalesOfLoansNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:to="lab_us-gaap_GainLossOnSalesOfLoansNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019ff14a-1b48-704a-946a-7089bd2c78b0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember_019ff14a-1aa9-7c53-a95f-febc0c79831e_terseLabel_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset management and subordinated performance fee</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember_label_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management and Subordinated Performance Fee [Member]</link:label>
    <link:label id="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember_documentation_en-US" xlink:label="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management and Subordinated Performance Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:href="bsprt-20260930.xsd#bsprt_AssetManagementAndSubordinatedPerformanceFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:to="lab_bsprt_AssetManagementAndSubordinatedPerformanceFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_019ff14a-1aa9-7660-92f6-8a5156d1c4f8_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccountsPayableAndAccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_019ff14a-1b48-7a18-b243-6672c7b6b57a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash payments for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, before Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaid" xlink:to="lab_us-gaap_IncomeTaxesPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_019ff14a-1b49-7f53-9e77-8ed87c7fc9f8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other segment items</link:label>
    <link:label id="lab_us-gaap_SegmentReportingOtherItemAmount_label_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingOtherItemAmount" xlink:to="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019ff14a-1c3b-7656-be93-3dfbe38ceeb1_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_019ff14a-1bcb-7c21-842d-6a5d22796217_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019ff14a-1bcb-7d5a-bac9-588786b246b5_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_019ff14a-1b49-7fc0-981a-93546cbcdd11_terseLabel_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Past Due Loans</link:label>
    <link:label id="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PastDueFinancingReceivablesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:to="lab_us-gaap_PastDueFinancingReceivablesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_019ff14a-1bcb-77bb-b72c-bc079ce060bf_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_019ff14a-1b49-7081-bb70-1437f3799b99_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssets" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayable_019ff14a-1b49-73e4-afd4-206f3583f3f7_netLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Mortgage note payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_019ff14a-1b49-7047-b2e0-fd02342a0283_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Par Value</link:label>
    <link:label id="lab_us-gaap_NotesPayable_019ff14a-1b49-703e-b998-c367f45b815f_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayable_label_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayable" xlink:to="lab_us-gaap_NotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditLossStatusAxis_019ff14a-1bcb-7aaf-9289-2825e13b6d50_terseLabel_en-US" xlink:label="lab_us-gaap_CreditLossStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditLossStatusAxis_label_en-US" xlink:label="lab_us-gaap_CreditLossStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Loss Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditLossStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditLossStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditLossStatusAxis" xlink:to="lab_us-gaap_CreditLossStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProductConcentrationRiskMember_019ff14a-1bcb-7cd8-9428-d9349b0343bb_terseLabel_en-US" xlink:label="lab_us-gaap_ProductConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product Concentration Risk</link:label>
    <link:label id="lab_us-gaap_ProductConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_ProductConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProductConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductConcentrationRiskMember" xlink:to="lab_us-gaap_ProductConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_019ff14a-1bcb-729a-ade8-1a6995f7e246_terseLabel_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MRAs</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_label_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreement [Member]</link:label>
    <link:label id="lab_bsprt_MasterRepurchaseAgreementMember_documentation_en-US" xlink:label="lab_bsprt_MasterRepurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Master Repurchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MasterRepurchaseAgreementMember" xlink:href="bsprt-20260930.xsd#bsprt_MasterRepurchaseAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MasterRepurchaseAgreementMember" xlink:to="lab_bsprt_MasterRepurchaseAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecurities_019ff14a-1b48-7224-8a07-b59257210f27_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral Pledged</link:label>
    <link:label id="lab_us-gaap_DebtSecurities_label_en-US" xlink:label="lab_us-gaap_DebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecurities" xlink:to="lab_us-gaap_DebtSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019ff14a-1b49-77c9-9d1b-d340ec41b840_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_September2021MultifamilyMember_01a15304-f074-79da-abf8-0033dde58b6f_terseLabel_en-US" xlink:label="lab_bsprt_September2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">September 2021 Multifamily</link:label>
    <link:label id="lab_bsprt_September2021MultifamilyMember_label_en-US" xlink:label="lab_bsprt_September2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">September 2021 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_September2021MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_September2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">September 2021 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_September2021MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_September2021MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_September2021MultifamilyMember" xlink:to="lab_bsprt_September2021MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FairValueInputsYield_019ff14a-1aa9-7c87-91f5-ccb98f498ccc_terseLabel_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Yield (percentage)</link:label>
    <link:label id="lab_bsprt_FairValueInputsYield_label_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Yield</link:label>
    <link:label id="lab_bsprt_FairValueInputsYield_documentation_en-US" xlink:label="lab_bsprt_FairValueInputsYield" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Inputs, Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FairValueInputsYield" xlink:href="bsprt-20260930.xsd#bsprt_FairValueInputsYield"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FairValueInputsYield" xlink:to="lab_bsprt_FairValueInputsYield" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement_01a164cd-d039-7a8b-8fad-357e6ad29bff_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, at fair value, Net Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueAfterOffsetAndDeductionSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_019ff14a-1c3b-7102-8eac-41d733e68db0_terseLabel_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_label_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:label id="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve_documentation_en-US" xlink:label="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Sharing Obligations, Allowance, Specific Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:href="bsprt-20260930.xsd#bsprt_LossSharingObligationsAllowanceSpecificReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:to="lab_bsprt_LossSharingObligationsAllowanceSpecificReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019ff14a-1c3c-7933-a5cc-a93a9e62b413_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization and Business Operations</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_019ff14a-1b49-73b7-a37a-270187bada6d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019ff14a-1bcb-7cf0-b840-287ff6239313_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_019ff14a-1b49-7d6c-bf0a-ba0ca620b222_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther_019ff14a-1bcb-7195-8b07-884e4a70dee7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Other Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_019ff14a-1bcb-75b5-bdab-f5acb688f1c8_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, net</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgage Servicing Rights, Net</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Mortgage Servicing Rights, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:to="lab_bsprt_BusinessCombinationRecognizedAssetAcquiredMortgageServicingRightsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019ff14a-1b49-73c9-bebe-b71773ffb04c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019ff14a-1bcb-73a2-94ae-2199a169f230_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_019ff14a-1bcb-7f92-95bb-f80df0ad2593_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Compensation and benefits</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_019ff14a-1b48-77e8-94bf-2e6fb69ee2d1_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net lease cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_019ff14a-1b49-76e1-8a8f-6f712116c14a_terseLabel_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales of investment securities, held to maturity</link:label>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_label_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sales Of Pledged Investment Securities</link:label>
    <link:label id="lab_bsprt_SalesOfPledgedInvestmentSecurities_documentation_en-US" xlink:label="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sales Of Pledged Investment Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SalesOfPledgedInvestmentSecurities" xlink:href="bsprt-20260930.xsd#bsprt_SalesOfPledgedInvestmentSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SalesOfPledgedInvestmentSecurities" xlink:to="lab_bsprt_SalesOfPledgedInvestmentSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_019ff14a-1bcb-7257-9cc7-2a6a88fcb0aa_terseLabel_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic Numerator</link:label>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_label_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basic Numerator [Abstract]</link:label>
    <link:label id="lab_bsprt_BasicNumeratorAbstract_documentation_en-US" xlink:label="lab_bsprt_BasicNumeratorAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Numerator [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BasicNumeratorAbstract" xlink:href="bsprt-20260930.xsd#bsprt_BasicNumeratorAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BasicNumeratorAbstract" xlink:to="lab_bsprt_BasicNumeratorAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_019ff14a-1bcb-7f79-9823-9f2dd8a4bf4f_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due to affiliates</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToAffiliates_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Due to Affiliates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDueToAffiliates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:to="lab_us-gaap_IncreaseDecreaseInDueToAffiliates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral_019ff14a-1bcb-7897-8283-17672027cbee_totalLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, Net Amount</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Including Not Subject to Master Netting Arrangement, after Offset and Deduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAmountOffsetAgainstCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019ff14a-1bcb-7014-99cb-b783870ee600_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic earnings per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember_019ff14a-1bcb-7b2c-af81-7e3862f38e89_terseLabel_en-US" xlink:label="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency loans</link:label>
    <link:label id="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember_label_en-US" xlink:label="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Sponsored-Enterprise Insured Loans [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:to="lab_us-gaap_UsGovernmentSponsoredEnterpriseInsuredLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BenefitStreetPartnersMember_019ff14a-1bcb-7a55-bb4d-477e57773bf5_terseLabel_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit Street Partners</link:label>
    <link:label id="lab_bsprt_BenefitStreetPartnersMember_label_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefit Street Partners [Member]</link:label>
    <link:label id="lab_bsprt_BenefitStreetPartnersMember_documentation_en-US" xlink:label="lab_bsprt_BenefitStreetPartnersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Benefit Street Partners</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BenefitStreetPartnersMember" xlink:href="bsprt-20260930.xsd#bsprt_BenefitStreetPartnersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BenefitStreetPartnersMember" xlink:to="lab_bsprt_BenefitStreetPartnersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_March2021MultifamilyMember_01a15303-9a16-73e7-aa64-ef4e51387919_terseLabel_en-US" xlink:label="lab_bsprt_March2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">March 2021 Multifamily</link:label>
    <link:label id="lab_bsprt_March2021MultifamilyMember_label_en-US" xlink:label="lab_bsprt_March2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">March 2021 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_March2021MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_March2021MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">March 2021 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_March2021MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_March2021MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_March2021MultifamilyMember" xlink:to="lab_bsprt_March2021MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_019ff14a-1bcb-71fe-81bd-13a853ccd1aa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments of deferred financing costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Financing Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfFinancingCosts" xlink:to="lab_us-gaap_PaymentsOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_019ff14a-1b49-78a8-8cc0-d310d39b56ff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Repurchases</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Treasury Stock [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfTreasuryStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_019ff14a-1aa9-79d3-b65f-4908af6d4a18_terseLabel_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition expenses</link:label>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_label_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquisition Expenses [Member]</link:label>
    <link:label id="lab_bsprt_AcquisitionExpensesMember_documentation_en-US" xlink:label="lab_bsprt_AcquisitionExpensesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Acquisition Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_AcquisitionExpensesMember" xlink:href="bsprt-20260930.xsd#bsprt_AcquisitionExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_AcquisitionExpensesMember" xlink:to="lab_bsprt_AcquisitionExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_019ff14a-1b49-7933-8849-3c58420b4bc5_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019ff14a-1b49-7cbc-9c66-02a47bcb6ace_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent_019ff14a-1aa9-7d4e-b453-5e4ab93600cb_terseLabel_en-US" xlink:label="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advance rate of mortgage loan (percent)</link:label>
    <link:label id="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent_label_en-US" xlink:label="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line Of Credit, Advance Rate Of Mortgage Loan, Percent</link:label>
    <link:label id="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent_documentation_en-US" xlink:label="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long-Term Line Of Credit, Advance Rate Of Mortgage Loan, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:href="bsprt-20260930.xsd#bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:to="lab_bsprt_LongTermLineOfCreditAdvanceRateOfMortgageLoanPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_019ff14a-1bcb-7467-9be8-a46863195cd9_terseLabel_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit</link:label>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_FifthThirdLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_FifthThirdLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fifth Third Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FifthThirdLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_FifthThirdLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FifthThirdLineOfCreditMember" xlink:to="lab_bsprt_FifthThirdLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_019ff14a-1aa9-7392-be08-ed948e55f033_terseLabel_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dispositions</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_label_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Dispositions</link:label>
    <link:label id="lab_bsprt_MortgageLoansOnRealEstateDispositions_documentation_en-US" xlink:label="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans On Real Estate, Dispositions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MortgageLoansOnRealEstateDispositions" xlink:href="bsprt-20260930.xsd#bsprt_MortgageLoansOnRealEstateDispositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MortgageLoansOnRealEstateDispositions" xlink:to="lab_bsprt_MortgageLoansOnRealEstateDispositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019ff14a-1b48-7bb3-ae47-8d196ff9486e_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019ff14a-1b48-72b2-b34b-edef5818e551_verboseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">% of Portfolio</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_019ff14a-1b49-7c96-8905-57aeb1eb8d63_terseLabel_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_label_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements Commercial Mortgage Loans</link:label>
    <link:label id="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans_documentation_en-US" xlink:label="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements Commercial Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:href="bsprt-20260930.xsd#bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:to="lab_bsprt_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsCommercialMortgageLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock_019ff14a-1bcb-782f-9fff-a11e29f7947f_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unfunded Commitments Under Commercial Mortgage Loans, Held for Investment</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligations Disclosure [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan_019ff14a-1c3b-76ac-9efc-a932b15a5a92_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fund</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Funded (Unfunded) Status of Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanFundedStatusOfPlan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:to="lab_us-gaap_DefinedBenefitPlanFundedStatusOfPlan" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019ff14a-1b49-747b-9999-52a62fdd0fa8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_019ff14a-1b49-796c-979c-01e68428d481_terseLabel_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Future Minimum Payments to be Received</link:label>
    <link:label id="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessor, Operating Lease, Payment to be Received, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:to="lab_us-gaap_LessorOperatingLeasePaymentsToBeReceivedMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_019ff14a-1b49-751d-8968-8a555bd627e3_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_019ff14a-1b49-72e7-83bc-f27a88a45697_terseLabel_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit</link:label>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_label_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit [Member]</link:label>
    <link:label id="lab_bsprt_PNCWHLineOfCreditMember_documentation_en-US" xlink:label="lab_bsprt_PNCWHLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">PNC WH Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PNCWHLineOfCreditMember" xlink:href="bsprt-20260930.xsd#bsprt_PNCWHLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PNCWHLineOfCreditMember" xlink:to="lab_bsprt_PNCWHLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_JPMorganSecuritiesLLCMember_019ff14a-1bcb-7de9-a291-78d809b2ed55_terseLabel_en-US" xlink:label="lab_bsprt_JPMorganSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">JP Morgan Securities LLC</link:label>
    <link:label id="lab_bsprt_JPMorganSecuritiesLLCMember_label_en-US" xlink:label="lab_bsprt_JPMorganSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">JP Morgan Securities LLC [Member]</link:label>
    <link:label id="lab_bsprt_JPMorganSecuritiesLLCMember_documentation_en-US" xlink:label="lab_bsprt_JPMorganSecuritiesLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">JP Morgan Securities LLC [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_JPMorganSecuritiesLLCMember" xlink:href="bsprt-20260930.xsd#bsprt_JPMorganSecuritiesLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_JPMorganSecuritiesLLCMember" xlink:to="lab_bsprt_JPMorganSecuritiesLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019ff14a-1b49-79b4-8d82-d8b3e520e06e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans Receivable by Class</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DurhamNorthCarolina2Member_01a1534f-b474-7ff8-a6b2-85c595df1997_terseLabel_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Durham, NC</link:label>
    <link:label id="lab_bsprt_DurhamNorthCarolina2Member_label_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Durham, North Carolina 2 [Member]</link:label>
    <link:label id="lab_bsprt_DurhamNorthCarolina2Member_documentation_en-US" xlink:label="lab_bsprt_DurhamNorthCarolina2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Durham, North Carolina 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DurhamNorthCarolina2Member" xlink:href="bsprt-20260930.xsd#bsprt_DurhamNorthCarolina2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DurhamNorthCarolina2Member" xlink:to="lab_bsprt_DurhamNorthCarolina2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyLossInPeriod_019ff14a-1bcb-7233-8f80-e0e75ad10b6f_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyLossInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision/(benefit) for loss sharing</link:label>
    <link:label id="lab_us-gaap_LossContingencyLossInPeriod_label_en-US" xlink:label="lab_us-gaap_LossContingencyLossInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Loss (Reversal of Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyLossInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyLossInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyLossInPeriod" xlink:to="lab_us-gaap_LossContingencyLossInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MSRepoFacilityMember_019ff14a-1c3b-751a-9731-2927e017d127_terseLabel_en-US" xlink:label="lab_bsprt_MSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MS Repo Facility</link:label>
    <link:label id="lab_bsprt_MSRepoFacilityMember_label_en-US" xlink:label="lab_bsprt_MSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MS Repo Facility [Member]</link:label>
    <link:label id="lab_bsprt_MSRepoFacilityMember_documentation_en-US" xlink:label="lab_bsprt_MSRepoFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">MS Repo Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MSRepoFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_MSRepoFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MSRepoFacilityMember" xlink:to="lab_bsprt_MSRepoFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019ff14a-1c3c-7928-bfa0-af097e0e360c_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite lived intangibles:</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLongTermDebt_019ff14a-1c3c-75f5-8a55-ef26c44961e3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
    <link:label id="lab_us-gaap_OtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_OtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLongTermDebt" xlink:to="lab_us-gaap_OtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_GeneralReserveMember_019ff14a-1b49-7f50-b4f7-a15daad2bef1_terseLabel_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General Reserve</link:label>
    <link:label id="lab_bsprt_GeneralReserveMember_label_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General Reserve [Member]</link:label>
    <link:label id="lab_bsprt_GeneralReserveMember_documentation_en-US" xlink:label="lab_bsprt_GeneralReserveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">General Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_GeneralReserveMember" xlink:href="bsprt-20260930.xsd#bsprt_GeneralReserveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_GeneralReserveMember" xlink:to="lab_bsprt_GeneralReserveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfFirstMortgageBond_019ff14a-1bcb-70f8-b692-b339210215d4_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfFirstMortgageBond" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage bankers bond</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfFirstMortgageBond_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfFirstMortgageBond" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of First Mortgage Bond</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfFirstMortgageBond" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfFirstMortgageBond"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfFirstMortgageBond" xlink:to="lab_us-gaap_RepaymentsOfFirstMortgageBond" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_019ff14a-1bcb-747e-9be9-a87794c8db9d_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_019ff14a-1bcb-7e55-8113-e2d5a81cd478_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">MSR payoffs</link:label>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_label_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay Offs Mortgage Servicing Rights MSRs</link:label>
    <link:label id="lab_bsprt_PayOffsMortgageServicingRightsMSRs_documentation_en-US" xlink:label="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Pay Offs Mortgage Servicing Rights MSRs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:href="bsprt-20260930.xsd#bsprt_PayOffsMortgageServicingRightsMSRs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:to="lab_bsprt_PayOffsMortgageServicingRightsMSRs" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VariableInterestEntityAssets_019ff14a-1c3c-7249-84b7-183ba147217d_terseLabel_en-US" xlink:label="lab_bsprt_VariableInterestEntityAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable interest entity (&#8220;VIE&#8221;) assets, measured at fair value</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityAssets_label_en-US" xlink:label="lab_bsprt_VariableInterestEntityAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Assets</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityAssets_documentation_en-US" xlink:label="lab_bsprt_VariableInterestEntityAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VariableInterestEntityAssets" xlink:href="bsprt-20260930.xsd#bsprt_VariableInterestEntityAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VariableInterestEntityAssets" xlink:to="lab_bsprt_VariableInterestEntityAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_019ff14a-1b49-70e2-ae6d-a4be9ddadd66_terseLabel_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension period on initial maturity date</link:label>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_label_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension On Initial Maturity Date</link:label>
    <link:label id="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate_documentation_en-US" xlink:label="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Extension on Initial Maturity Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:href="bsprt-20260930.xsd#bsprt_DebtInstrumentExtensionOnInitialMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:to="lab_bsprt_DebtInstrumentExtensionOnInitialMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019ff14a-1bcb-781c-9bb8-dd4025516701_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019ff14a-1bcb-774c-a550-4d7051be57ed_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Administrative services expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019ff14a-1aa9-7a08-894d-863f19b1648e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_019ff14a-1b49-70d6-8b88-04beb8d7eec4_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of real estate properties</link:label>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_label_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfRealEstateProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfRealEstateProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfRealEstateProperties" xlink:to="lab_us-gaap_NumberOfRealEstateProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_019ff14a-1b48-731f-b42e-4b032ae5d095_verboseLabel_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements - commercial mortgage loans</link:label>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_019ff14a-1b48-7925-b81a-e2e1df9adcf0_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, commercial mortgage loans</link:label>
    <link:label id="lab_us-gaap_CommercialMortgageBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Mortgage-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommercialMortgageBackedSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:to="lab_us-gaap_CommercialMortgageBackedSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_VariableInterestEntityIncomeLoss_019ff14a-1c3c-7f2b-8a14-6c96b6562a8b_terseLabel_en-US" xlink:label="lab_bsprt_VariableInterestEntityIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net assets of consolidated VIE, CMBS trust</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityIncomeLoss_label_en-US" xlink:label="lab_bsprt_VariableInterestEntityIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Income (loss)</link:label>
    <link:label id="lab_bsprt_VariableInterestEntityIncomeLoss_documentation_en-US" xlink:label="lab_bsprt_VariableInterestEntityIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity Income (loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_VariableInterestEntityIncomeLoss" xlink:href="bsprt-20260930.xsd#bsprt_VariableInterestEntityIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_VariableInterestEntityIncomeLoss" xlink:to="lab_bsprt_VariableInterestEntityIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_019ff14a-1c3c-759b-9cf6-af8895566958_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ShareRepurchaseProgramAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramAxis" xlink:to="lab_srt_ShareRepurchaseProgramAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019ff14a-1bcb-730a-9bec-0d3d26fa8979_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019ff14a-1c3b-76c4-ae06-5d386bb4abb0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_019ff14a-1b48-7b5f-b55f-0423981d58c8_terseLabel_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025-FL12 Issuer</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_label_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2024-FL11 Issuer [Member]</link:label>
    <link:label id="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember_documentation_en-US" xlink:label="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations Issued in 2024-FL11 Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:href="bsprt-20260930.xsd#bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:to="lab_bsprt_CollateralizedLoanObligationsIssuedIn2024FL11IssuerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_June2022MultifamilyMember_019ff14a-1bcb-76a4-a39e-1cbcacc8c72d_terseLabel_en-US" xlink:label="lab_bsprt_June2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">June 2021 Multifamily</link:label>
    <link:label id="lab_bsprt_June2022MultifamilyMember_label_en-US" xlink:label="lab_bsprt_June2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">June 2022 Multifamily [Member]</link:label>
    <link:label id="lab_bsprt_June2022MultifamilyMember_documentation_en-US" xlink:label="lab_bsprt_June2022MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">June 2022 Multifamily</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_June2022MultifamilyMember" xlink:href="bsprt-20260930.xsd#bsprt_June2022MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_June2022MultifamilyMember" xlink:to="lab_bsprt_June2022MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentsJointVentures_019ff14a-1aa9-7bb4-a676-dbf4fa03f567_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentsJointVentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments, joint ventures</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentsJointVentures_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentsJointVentures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments, Joint Ventures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentsJointVentures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateInvestmentsJointVentures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentsJointVentures" xlink:to="lab_us-gaap_RealEstateInvestmentsJointVentures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_019ff14a-1bcb-7947-b0ce-c282e285d3bc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Shares Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SalesRevenueProductLineMember_019ff14a-1bcb-7f93-9c57-7b9b18cf647c_terseLabel_en-US" xlink:label="lab_us-gaap_SalesRevenueProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Product and Service Benchmark</link:label>
    <link:label id="lab_us-gaap_SalesRevenueProductLineMember_label_en-US" xlink:label="lab_us-gaap_SalesRevenueProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Product and Service Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SalesRevenueProductLineMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesRevenueProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SalesRevenueProductLineMember" xlink:to="lab_us-gaap_SalesRevenueProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_019ff14a-1aa9-7872-b845-77bf2882dfca_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc.</link:label>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_label_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysCapitalIncMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysCapitalIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Capital Inc [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BarclaysCapitalIncMember" xlink:href="bsprt-20260930.xsd#bsprt_BarclaysCapitalIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BarclaysCapitalIncMember" xlink:to="lab_bsprt_BarclaysCapitalIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_019ff14a-1bcb-7e3c-b80f-4e2fe50451c4_negatedTerseLabel_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of real estate owned and capital expenditures</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_label_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Real Estate Owned</link:label>
    <link:label id="lab_bsprt_PaymentsToAcquireRealEstateOwned_documentation_en-US" xlink:label="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_PaymentsToAcquireRealEstateOwned" xlink:href="bsprt-20260930.xsd#bsprt_PaymentsToAcquireRealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_PaymentsToAcquireRealEstateOwned" xlink:to="lab_bsprt_PaymentsToAcquireRealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_019ff14a-1b48-7fa9-b656-dcdeda0bf507_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned, net of depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateAcquiredThroughForeclosure_label_en-US" xlink:label="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Acquired Through Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RealEstateAcquiredThroughForeclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:to="lab_us-gaap_RealEstateAcquiredThroughForeclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ReserveQuantitiesByTypeOfReserveAxis_019ff14a-1b49-7f14-bd4e-61bbe07ee937_terseLabel_en-US" xlink:label="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Petroleum Reserves [Axis]</link:label>
    <link:label id="lab_srt_ReserveQuantitiesByTypeOfReserveAxis_label_en-US" xlink:label="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Petroleum Reserves [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ReserveQuantitiesByTypeOfReserveAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:to="lab_srt_ReserveQuantitiesByTypeOfReserveAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_019ff14a-1bcb-7e2f-9d04-c16f4f510376_terseLabel_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing portfolio</link:label>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_label_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Loan Servicing Portfolio</link:label>
    <link:label id="lab_bsprt_FinancingReceivableLoanServicingPortfolio_documentation_en-US" xlink:label="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Loan Servicing Portfolio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:href="bsprt-20260930.xsd#bsprt_FinancingReceivableLoanServicingPortfolio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:to="lab_bsprt_FinancingReceivableLoanServicingPortfolio" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019ff14a-1aa9-7e8c-b859-5be18f4915c3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Purchase Price</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019ff14a-1aa9-7729-862f-117f5ed7a24f_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Purchase price</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019ff14a-1bcb-737d-abde-1907232e538f_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_019ff14a-1b48-7477-8cbb-612d4898046a_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowElementsAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Elements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowElementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowElementsAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowElementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_MixedUseMember_019ff14a-1bcb-77bc-bc5b-acfcc9aed99d_terseLabel_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mixed Use</link:label>
    <link:label id="lab_bsprt_MixedUseMember_label_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mixed Use [Member]</link:label>
    <link:label id="lab_bsprt_MixedUseMember_documentation_en-US" xlink:label="lab_bsprt_MixedUseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mixed Use [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_MixedUseMember" xlink:href="bsprt-20260930.xsd#bsprt_MixedUseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_MixedUseMember" xlink:to="lab_bsprt_MixedUseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_019ff14a-1aa9-7dd5-b6b3-d12dc1b88817_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of software development costs</link:label>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_label_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Develop Software</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToDevelopSoftware" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToDevelopSoftware"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToDevelopSoftware" xlink:to="lab_us-gaap_PaymentsToDevelopSoftware" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_019ff14a-1b49-791d-9bbd-604f995e7fe6_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Offsetting Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_OffsettingLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019ff14a-1aa9-710a-ab4a-afce28fa24f9_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized Gain/(Loss)</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019ff14a-1bcb-7f7a-b792-6e78e70183e1_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_019ff14a-1b49-7d65-9300-ed882bec260c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_019ff14a-1b48-7199-bf9f-770bdfd27438_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions from equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentDividendsOrDistributions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:to="lab_us-gaap_EquityMethodInvestmentDividendsOrDistributions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_019ff14a-1b49-7267-8dd1-e25a26cbff71_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoanPurchaseCommitmentsMember_019ff14a-1bcb-7a1d-a30b-ea6c9c716d31_terseLabel_en-US" xlink:label="lab_us-gaap_LoanPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan commitments</link:label>
    <link:label id="lab_us-gaap_LoanPurchaseCommitmentsMember_label_en-US" xlink:label="lab_us-gaap_LoanPurchaseCommitmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Purchase Commitments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanPurchaseCommitmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoanPurchaseCommitmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanPurchaseCommitmentsMember" xlink:to="lab_us-gaap_LoanPurchaseCommitmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset_019ff14a-1aa9-73ed-95c0-60af4e6ab03f_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, Gross Amounts Offset on the Balance Sheet</link:label>
    <link:label id="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset_label_en-US" xlink:label="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Sold under Agreement to Repurchase, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:to="lab_us-gaap_SecuritiesSoldUnderAgreementsToRepurchaseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_019ff14a-1aa9-7431-a25e-77d988fed417_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019ff14a-1bcb-734a-a700-a797017f0269_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_019ff14a-1aa9-79e4-8cfa-5b8157dcf0ba_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019ff14a-1aa9-7eab-8cd2-5c5f5afac09b_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income/(loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_019ff14a-1b48-7a2d-9e18-df6ee8b93b3e_terseLabel_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barclays Revolver Facility</link:label>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_label_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barclays Revolver Facility [Member]</link:label>
    <link:label id="lab_bsprt_BarclaysRevolverFacilityMember_documentation_en-US" xlink:label="lab_bsprt_BarclaysRevolverFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barclays Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_BarclaysRevolverFacilityMember" xlink:href="bsprt-20260930.xsd#bsprt_BarclaysRevolverFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_BarclaysRevolverFacilityMember" xlink:to="lab_bsprt_BarclaysRevolverFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_HospitalityPropertyMember_019ff14a-1b49-7ee3-ad14-9cdee83c9872_terseLabel_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hospitality Property</link:label>
    <link:label id="lab_bsprt_HospitalityPropertyMember_label_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hospitality Property [Member]</link:label>
    <link:label id="lab_bsprt_HospitalityPropertyMember_documentation_en-US" xlink:label="lab_bsprt_HospitalityPropertyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Hospitality Property</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_HospitalityPropertyMember" xlink:href="bsprt-20260930.xsd#bsprt_HospitalityPropertyMember"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_019ff14a-1bcb-7dae-b53d-bd2467823a5f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_019ff14a-1bcb-776d-bda9-862521de40dd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative instruments, measured at fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019ff14a-1bcb-71e5-a277-a50b363f0fa2_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Treasury notes</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019ff14a-1aa9-74c9-aa1a-542df2bddc4c_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ff14a-1b48-7390-a9bf-8ab1ca923538_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">(Provision)/benefit for income tax</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_019ff14a-1b49-7346-ac3f-8d91da439d95_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series H Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesHPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesHPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series H Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesHPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SeriesHPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesHPreferredStockMember" xlink:to="lab_us-gaap_SeriesHPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualPayments_01a15fd1-7773-7571-a0a7-9dd186b7571c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Charge offs for specific allowance for loss sharing</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualPayments_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualPayments" xlink:to="lab_us-gaap_LossContingencyAccrualPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019ff14a-1c3b-7029-b2d0-563a108bb0b7_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_01a164c8-28e3-7ee9-b4d6-16fa4a735bca_terseLabel_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Liabilities</link:label>
    <link:label id="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting Derivative Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OffsettingDerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_OffsettingDerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_019ff14a-1bcb-7179-a437-eabb9e15d3f6_terseLabel_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other financings</link:label>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_label_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Note-on-Note Financing [Member]</link:label>
    <link:label id="lab_bsprt_NoteOnNoteFinancingMember_documentation_en-US" xlink:label="lab_bsprt_NoteOnNoteFinancingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Note-on-Note Financing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NoteOnNoteFinancingMember" xlink:href="bsprt-20260930.xsd#bsprt_NoteOnNoteFinancingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NoteOnNoteFinancingMember" xlink:to="lab_bsprt_NoteOnNoteFinancingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019ff14a-1bcb-7df9-8720-8931cbd0b4e7_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_019ff14a-1c3b-79ad-b7d5-80ffc5f5496c_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_label_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AOCIAttributableToParentNetOfTaxRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:to="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019ff14a-1b49-79ec-98a8-ed369ab4bb07_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted Cash Flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_NonaccrualMember_01a1668a-d59b-7686-8bdd-dd81ca44b719_terseLabel_en-US" xlink:label="lab_bsprt_NonaccrualMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nonaccrual</link:label>
    <link:label id="lab_bsprt_NonaccrualMember_label_en-US" xlink:label="lab_bsprt_NonaccrualMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonaccrual [Member]</link:label>
    <link:label id="lab_bsprt_NonaccrualMember_documentation_en-US" xlink:label="lab_bsprt_NonaccrualMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_NonaccrualMember" xlink:href="bsprt-20260930.xsd#bsprt_NonaccrualMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_NonaccrualMember" xlink:to="lab_bsprt_NonaccrualMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable_019ff14a-1bcb-7c94-a72a-e6bb279c7b6b_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal repayments received on commercial mortgage loans, held for investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection of Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromCollectionOfLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:to="lab_us-gaap_ProceedsFromCollectionOfLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019ff14a-1bcb-76ea-bf1a-9d348b092c67_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_019ff14a-1b49-7409-93f1-1ebc392f434e_terseLabel_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 and beyond</link:label>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_label_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, after Year Four and After Year Four</link:label>
    <link:label id="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour_documentation_en-US" xlink:label="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation, to be Paid, Year Four and After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:href="bsprt-20260930.xsd#bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:to="lab_bsprt_UnrecordedUnconditionalPurchaseObligationToBePaidAfterYearFourAndAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_SubsequentReturnHurdleRateMember_01a16143-99c2-7396-b84b-b4c6d0e4c2d5_terseLabel_en-US" xlink:label="lab_bsprt_SubsequentReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Return Hurdle Rate</link:label>
    <link:label id="lab_bsprt_SubsequentReturnHurdleRateMember_label_en-US" xlink:label="lab_bsprt_SubsequentReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Return Hurdle Rate [Member]</link:label>
    <link:label id="lab_bsprt_SubsequentReturnHurdleRateMember_documentation_en-US" xlink:label="lab_bsprt_SubsequentReturnHurdleRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subsequent Return Hurdle Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_SubsequentReturnHurdleRateMember" xlink:href="bsprt-20260930.xsd#bsprt_SubsequentReturnHurdleRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_SubsequentReturnHurdleRateMember" xlink:to="lab_bsprt_SubsequentReturnHurdleRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_019ff14a-1b49-7057-8a9c-a17e12935017_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year two, originated in prior fiscal year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearTwoOriginatedFiscalYearBeforeCurrentFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_019ff14a-1c3b-734b-8ffa-cb7793c98190_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Loans on Nonaccrual Status</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Nonaccrual [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesNonAccrualStatusTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment_01a0677e-1dc4-7b73-aceb-6eb06045b821_terseLabel_en-US" xlink:label="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans transferred from commercial mortgage loans, held for investment to commercial mortgage loans, held for sale</link:label>
    <link:label id="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment_label_en-US" xlink:label="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Transferred To Commercial Mortgage Loans, Held-for-Investment</link:label>
    <link:label id="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment_documentation_en-US" xlink:label="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Transferred To Commercial Mortgage Loans, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:href="bsprt-20260930.xsd#bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:to="lab_bsprt_LoansTransferredToCommercialMortgageLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_019ff14a-1b49-7760-a272-9c5ca2101813_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_019ff14a-1b49-7b27-ba82-d668f826af55_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts of Recognized Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock_019ff14a-1b48-7e9e-97d0-a0db8f073d16_terseLabel_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Owned, Held For Investment</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock_label_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment [Table Text Block]</link:label>
    <link:label id="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock_documentation_en-US" xlink:label="lab_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Held For Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock" xlink:href="bsprt-20260930.xsd#bsprt_RealEstateOwnedHeldForInvestmentTableTextBlock"/>
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