Tax Receivable Agreement and Income Taxes - Schedule of Provision for Income Taxes (Details) - USD ($)		3 Months Ended			9 Months Ended		12 Months Ended
	Jan. 01, 2023	Sep. 30, 2024	Dec. 31, 2023	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Provision for income taxes
Income tax expense		$ 6,606,000		$ 166,000	$ 6,132,000	$ 166,000	$ 568,000	$ 246,000	$ 0
Corporation income tax rate (in percent)	20.45%	2884.70%	23.35%	4.70%	(85.10%)	4.90%