Equity and Earnings Per Share - Schedule of Weighted Average Shares of Fully Diluted Basis (Details) - shares	1 Months Ended	2 Months Ended	3 Months Ended
Jun. 06, 2025	Jul. 31, 2025	Jul. 31, 2026
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Common shares outstanding (in shares)	1,410	842,852	41,599,572
Common share equivalents (in shares)	0	0	11,314,872
Weighted-average number of common shares outstanding – basic (in shares)	1,410	842,852	52,914,444
Dilutive shares (in shares)	0	670,651	51,414,101
Weighted-averages shares on a fully diluted basis (in shares)	1,410	1,513,503	104,328,545
Pre-funded Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Common share equivalents (in shares)	0	0	7,750,510
Strategic Advisor Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Common share equivalents (in shares)	0	0	3,564,362
Warrant
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	607,517	50,990,135
Warrant \| Stapled Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	0	49,504,988
Warrant \| Asset Manager Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	0	990,099
Warrant \| Public Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	519,959	409,117
Warrant \| 2022 Underwriter Warrants
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	87,558	85,931
RSUs
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	1,175	364,966
Stock options
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	22,109	16,574
Convertible note
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Dilutive shares (in shares)	0	39,850	42,426

Weighted Average Number of Shares Common Share Equivalents

No definition available.

Name:	bncww_WeightedAverageNumberOfSharesCommonShareEquivalents
Namespace Prefix:	bncww_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted Average Number Of Shares Outstanding, Diluted, Adjustment and Antidilutive Securities, Amount

+ References

No definition available.

+ Details

Name:	bncww_WeightedAverageNumberOfSharesOutstandingDilutedAdjustmentAndAntidilutiveSecuritiesAmount
Namespace Prefix:	bncww_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted Average Number of Shares Outstanding, Diluted Including Antidilutive Securities, Amount

+ References

No definition available.

+ Details

Name:	bncww_WeightedAverageNumberOfSharesOutstandingDilutedIncludingAntidilutiveSecuritiesAmount
Namespace Prefix:	bncww_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(v)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(iii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(iv)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (l)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 35
-Paragraph 1D
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480483/718-10-35-1D

Reference 11: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 35
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480483/718-10-35-3

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 15: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 16: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 17: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 18: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(01)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 19: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(02)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 20: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(03)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 21: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 22: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 23: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 24: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 25: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(01)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 26: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(02)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 27: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(03)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 28: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 29: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (e)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

Reference 30: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (e)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

This element represents the weighted average total number of shares issued throughout the period including the first (beginning balance outstanding) and last (ending balance outstanding) day of the period before considering any reductions (for instance, shares held in treasury) to arrive at the weighted average number of shares outstanding. Weighted average relates to the portion of time within a reporting period that common shares have been issued and outstanding to the total time in that period. Such concept is used in determining the weighted average number of shares outstanding for purposes of calculating earnings per share (basic).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482689/260-10-45-10

+ Details

Name:	us-gaap_WeightedAverageNumberOfSharesIssuedBasic
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of [basic] shares or units, after adjustment for contingently issuable shares or units and other shares or units not deemed outstanding, determined by relating the portion of time within a reporting period that common shares or units have been outstanding to the total time in that period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482662/260-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 260
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482689/260-10-45-10

+ Details

Name:	us-gaap_WeightedAverageNumberOfSharesOutstandingBasic
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_PrefundedWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_StrategicAdvisorWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis=us-gaap_WarrantMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_StapledWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_AssetManagerWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_PublicWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=bncww_TwoThousandAndTwentyTwoUnderwriterWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis=us-gaap_EmployeeStockOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis=us-gaap_ConvertibleDebtSecuritiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: