Net Loss Per Share - Schedule of securities were not included in the computation of diluted shares outstanding (Detail)	6 Months Ended
	Jun. 30, 2024 shares
PubCo Warrants - Public and Private
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	43,848,750
PubCo Class E Common Stock - Earnouts Units
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	1,075,761
BT OpCo Founder Convertible Preferred Units
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	2,900,000
BT OpCo Exchangeable Non-Controlling Interest
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	38,293,024
BT OpCo Earnouts Units
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	15,000,000
2023 Incentive Plan RSU awards
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Number of securities	2,127,818