<?xml version='1.0' encoding='utf-8'?>
<FilingSummary>
  <Version>3.26.1</Version>
  <ProcessingTime/>
  <ReportFormat>html</ReportFormat>
  <ContextCount>182</ContextCount>
  <ElementCount>291</ElementCount>
  <EntityCount>1</EntityCount>
  <FootnotesReported>false</FootnotesReported>
  <SegmentCount>78</SegmentCount>
  <ScenarioCount>0</ScenarioCount>
  <TuplesReported>false</TuplesReported>
  <UnitCount>5</UnitCount>
  <MyReports>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R1.htm</HtmlFileName>
      <LongName>000 - Document - Document And Entity Information</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/DocumentAndEntityInformation</Role>
      <ShortName>Document And Entity Information</ShortName>
      <MenuCategory>Cover</MenuCategory>
      <Position>1</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R2.htm</HtmlFileName>
      <LongName>001 - Statement - Consolidated Balance Sheets (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConsolidatedBalanceSheet</Role>
      <ShortName>Consolidated Balance Sheets (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>2</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R3.htm</HtmlFileName>
      <LongName>002 - Statement - Consolidated Balance Sheets (unaudited) (Parentheticals)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConsolidatedBalanceSheet_Parentheticals</Role>
      <ShortName>Consolidated Balance Sheets (unaudited) (Parentheticals)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>3</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R4.htm</HtmlFileName>
      <LongName>003 - Statement - Consolidated Statements of Operations (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConsolidatedIncomeStatement</Role>
      <ShortName>Consolidated Statements of Operations (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>4</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R5.htm</HtmlFileName>
      <LongName>004 - Statement - Consolidated Statements of Stockholders’ Deficit (Unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ShareholdersEquityType2or3</Role>
      <ShortName>Consolidated Statements of Stockholders’ Deficit (Unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>5</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R6.htm</HtmlFileName>
      <LongName>005 - Statement - Consolidated Statements of Cash Flows (unaudited)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConsolidatedCashFlow</Role>
      <ShortName>Consolidated Statements of Cash Flows (unaudited)</ShortName>
      <MenuCategory>Statements</MenuCategory>
      <Position>6</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R7.htm</HtmlFileName>
      <LongName>006 - Disclosure - Organization and Description of Business, Liquidity, and Risk Factors</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/OrganizationandDescriptionofBusinessLiquidityandRiskFactors</Role>
      <ShortName>Organization and Description of Business, Liquidity, and Risk Factors</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>7</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R8.htm</HtmlFileName>
      <LongName>007 - Disclosure - Significant Accounting Policies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SignificantAccountingPolicies</Role>
      <ShortName>Significant Accounting Policies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>8</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R9.htm</HtmlFileName>
      <LongName>008 - Disclosure - Related Party Transactions</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/RelatedPartyTransactions</Role>
      <ShortName>Related Party Transactions</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>9</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R10.htm</HtmlFileName>
      <LongName>009 - Disclosure - Convertible Debt</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConvertibleDebt</Role>
      <ShortName>Convertible Debt</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>10</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R11.htm</HtmlFileName>
      <LongName>010 - Disclosure - Tedco Grant</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/TedcoGrant</Role>
      <ShortName>Tedco Grant</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>11</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R12.htm</HtmlFileName>
      <LongName>011 - Disclosure - Commitments and Contingencies</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/CommitmentsandContingencies</Role>
      <ShortName>Commitments and Contingencies</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>12</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R13.htm</HtmlFileName>
      <LongName>012 - Disclosure - Equity</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/Equity</Role>
      <ShortName>Equity</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>13</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R14.htm</HtmlFileName>
      <LongName>013 - Disclosure - Redeemable Preferred Stock, Mezzanine Equity and Warrant Liability</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/RedeemablePreferredStockMezzanineEquityandWarrantLiability</Role>
      <ShortName>Redeemable Preferred Stock, Mezzanine Equity and Warrant Liability</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>14</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R15.htm</HtmlFileName>
      <LongName>014 - Disclosure - Segment and Geographic Information</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SegmentandGeographicInformation</Role>
      <ShortName>Segment and Geographic Information</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>15</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R16.htm</HtmlFileName>
      <LongName>015 - Disclosure - Subsequent Events</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SubsequentEvents</Role>
      <ShortName>Subsequent Events</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>16</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R17.htm</HtmlFileName>
      <LongName>995410 - Disclosure - Pay vs Performance Disclosure</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/PvpDisclosure</Role>
      <ShortName>Pay vs Performance Disclosure</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>17</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R18.htm</HtmlFileName>
      <LongName>995445 - Disclosure - Insider Trading Arrangements</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://xbrl.sec.gov/ecd/role/InsiderTradingArrangements</Role>
      <ShortName>Insider Trading Arrangements</ShortName>
      <MenuCategory>Notes</MenuCategory>
      <Position>18</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R19.htm</HtmlFileName>
      <LongName>996000 - Disclosure - Accounting Policies, by Policy (Policies)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/AccountingPoliciesByPolicy</Role>
      <ShortName>Accounting Policies, by Policy (Policies)</ShortName>
      <MenuCategory>Policies</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SignificantAccountingPolicies</ParentRole>
      <Position>19</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R20.htm</HtmlFileName>
      <LongName>996001 - Disclosure - Significant Accounting Policies (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SignificantAccountingPoliciesTables</Role>
      <ShortName>Significant Accounting Policies (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SignificantAccountingPolicies</ParentRole>
      <Position>20</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R21.htm</HtmlFileName>
      <LongName>996002 - Disclosure - Commitments and Contingencies (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/CommitmentsandContingenciesTables</Role>
      <ShortName>Commitments and Contingencies (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/CommitmentsandContingencies</ParentRole>
      <Position>21</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R22.htm</HtmlFileName>
      <LongName>996003 - Disclosure - Equity (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/EquityTables</Role>
      <ShortName>Equity (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/Equity</ParentRole>
      <Position>22</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R23.htm</HtmlFileName>
      <LongName>996004 - Disclosure - Segment and Geographic Information (Tables)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SegmentandGeographicInformationTables</Role>
      <ShortName>Segment and Geographic Information (Tables)</ShortName>
      <MenuCategory>Tables</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SegmentandGeographicInformation</ParentRole>
      <Position>23</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R24.htm</HtmlFileName>
      <LongName>996005 - Disclosure - Organization and Description of Business, Liquidity, and Risk Factors (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/OrganizationandDescriptionofBusinessLiquidityandRiskFactorsDetails</Role>
      <ShortName>Organization and Description of Business, Liquidity, and Risk Factors (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/OrganizationandDescriptionofBusinessLiquidityandRiskFactors</ParentRole>
      <Position>24</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R25.htm</HtmlFileName>
      <LongName>996006 - Disclosure - Significant Accounting Policies (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SignificantAccountingPoliciesDetails</Role>
      <ShortName>Significant Accounting Policies (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SignificantAccountingPoliciesTables</ParentRole>
      <Position>25</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R26.htm</HtmlFileName>
      <LongName>996007 - Disclosure - Significant Accounting Policies - Schedule of Fair Value of the Purchase Consideration (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofFairValueofthePurchaseConsiderationTable</Role>
      <ShortName>Significant Accounting Policies - Schedule of Fair Value of the Purchase Consideration (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>26</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R27.htm</HtmlFileName>
      <LongName>996008 - Disclosure - Significant Accounting Policies - Schedule of Fair Value of the Purchase Consideration (Parentheticals) (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofFairValueofthePurchaseConsiderationTable_Parentheticals</Role>
      <ShortName>Significant Accounting Policies - Schedule of Fair Value of the Purchase Consideration (Parentheticals) (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>27</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R28.htm</HtmlFileName>
      <LongName>996009 - Disclosure - Significant Accounting Policies - Schedule of Expected Future Amortization Expense (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofExpectedFutureAmortizationExpenseTable</Role>
      <ShortName>Significant Accounting Policies - Schedule of Expected Future Amortization Expense (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>28</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R29.htm</HtmlFileName>
      <LongName>996010 - Disclosure - Significant Accounting Policies - Schedule of Preferred Stock and Common Stock Equivalents (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofPreferredStockandCommonStockEquivalentsTable</Role>
      <ShortName>Significant Accounting Policies - Schedule of Preferred Stock and Common Stock Equivalents (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>29</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R30.htm</HtmlFileName>
      <LongName>996011 - Disclosure - Related Party Transactions (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/RelatedPartyTransactionsDetails</Role>
      <ShortName>Related Party Transactions (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/RelatedPartyTransactions</ParentRole>
      <Position>30</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R31.htm</HtmlFileName>
      <LongName>996012 - Disclosure - Convertible Debt (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ConvertibleDebtDetails</Role>
      <ShortName>Convertible Debt (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/ConvertibleDebt</ParentRole>
      <Position>31</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R32.htm</HtmlFileName>
      <LongName>996013 - Disclosure - Tedco Grant (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/TedcoGrantDetails</Role>
      <ShortName>Tedco Grant (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/TedcoGrant</ParentRole>
      <Position>32</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R33.htm</HtmlFileName>
      <LongName>996014 - Disclosure - Commitments and Contingencies (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/CommitmentsandContingenciesDetails</Role>
      <ShortName>Commitments and Contingencies (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/CommitmentsandContingenciesTables</ParentRole>
      <Position>33</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R34.htm</HtmlFileName>
      <LongName>996015 - Disclosure - Commitments and Contingencies - Schedule of Future Milestones (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofFutureMilestonesTable</Role>
      <ShortName>Commitments and Contingencies - Schedule of Future Milestones (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>34</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R35.htm</HtmlFileName>
      <LongName>996016 - Disclosure - Commitments and Contingencies - Schedule of Certain Fees and Corresponding Payment Amounts (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofCertainFeesandCorrespondingPaymentAmountsTable</Role>
      <ShortName>Commitments and Contingencies - Schedule of Certain Fees and Corresponding Payment Amounts (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>35</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R36.htm</HtmlFileName>
      <LongName>996017 - Disclosure - Equity (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/EquityDetails</Role>
      <ShortName>Equity (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/EquityTables</ParentRole>
      <Position>36</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R37.htm</HtmlFileName>
      <LongName>996018 - Disclosure - Equity - Schedule of Common Stock Options Issued (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofCommonStockOptionsIssuedTable</Role>
      <ShortName>Equity - Schedule of Common Stock Options Issued (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>37</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R38.htm</HtmlFileName>
      <LongName>996019 - Disclosure - Equity - Schedule of Black-Scholes Option Pricing Model (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofBlackScholesOptionPricingModelTable</Role>
      <ShortName>Equity - Schedule of Black-Scholes Option Pricing Model (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>38</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R39.htm</HtmlFileName>
      <LongName>996020 - Disclosure - Redeemable Preferred Stock, Mezzanine Equity and Warrant Liability (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/RedeemablePreferredStockMezzanineEquityandWarrantLiabilityDetails</Role>
      <ShortName>Redeemable Preferred Stock, Mezzanine Equity and Warrant Liability (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/RedeemablePreferredStockMezzanineEquityandWarrantLiability</ParentRole>
      <Position>39</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R40.htm</HtmlFileName>
      <LongName>996021 - Disclosure - Segment and Geographic Information (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SegmentandGeographicInformationDetails</Role>
      <ShortName>Segment and Geographic Information (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SegmentandGeographicInformationTables</ParentRole>
      <Position>40</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R41.htm</HtmlFileName>
      <LongName>996022 - Disclosure - Segment and Geographic Information - Schedule of Financial Information of Operating Segment (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/ScheduleofFinancialInformationofOperatingSegmentTable</Role>
      <ShortName>Segment and Geographic Information - Schedule of Financial Information of Operating Segment (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <Position>41</Position>
    </Report>
    <Report instance="ea0290259-10q_ostherap.htm">
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <HtmlFileName>R42.htm</HtmlFileName>
      <LongName>996023 - Disclosure - Subsequent Events (Details)</LongName>
      <ReportType>Sheet</ReportType>
      <Role>http://www.ostherapies.com/role/SubsequentEventsDetails</Role>
      <ShortName>Subsequent Events (Details)</ShortName>
      <MenuCategory>Details</MenuCategory>
      <ParentRole>http://www.ostherapies.com/role/SubsequentEvents</ParentRole>
      <Position>42</Position>
    </Report>
    <Report>
      <IsDefault>false</IsDefault>
      <HasEmbeddedReports>false</HasEmbeddedReports>
      <LongName>All Reports</LongName>
      <ReportType>Book</ReportType>
      <ShortName>All Reports</ShortName>
    </Report>
  </MyReports>
  <InputFiles>
    <File doctype="10-Q" isDefinitelyFs="true" isUsgaap="true" original="ea0290259-10q_ostherap.htm">ea0290259-10q_ostherap.htm</File>
    <File>osti-20260331.xsd</File>
    <File>osti-20260331_cal.xml</File>
    <File>osti-20260331_def.xml</File>
    <File>osti-20260331_lab.xml</File>
    <File>osti-20260331_pre.xml</File>
  </InputFiles>
  <SupplementalFiles/>
  <BaseTaxonomies>
    <BaseTaxonomy items="1">http://fasb.org/srt/2026</BaseTaxonomy>
    <BaseTaxonomy items="501">http://fasb.org/us-gaap/2026</BaseTaxonomy>
    <BaseTaxonomy items="32">http://xbrl.sec.gov/dei/2026</BaseTaxonomy>
    <BaseTaxonomy items="4">http://xbrl.sec.gov/ecd/2026</BaseTaxonomy>
  </BaseTaxonomies>
  <HasPresentationLinkbase>true</HasPresentationLinkbase>
  <HasCalculationLinkbase>true</HasCalculationLinkbase>
</FilingSummary>
