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Discontinued Operations - Summary of the Aggregate Carrying Amounts of Assets and Liabilities Held for Sale (Parenthetical) (Details) - USD ($) $ in Thousands	Dec. 31, 2025	Dec. 31, 2024
Community Living Business | Discontinued Operations
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]
Accumulated depreciation	$ 104,314	$ 110,417

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- Definition

Disposal group, including discontinued operation, accumulated depreciation of property, plant, and equipment.

+ References

No definition available.

+ Details

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Namespace Prefix:	btsg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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- 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 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3A
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482099/360-10-50-3A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3A
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482099/360-10-50-3A

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- Details

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- Details

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