Tax Receivable Agreement and Income Taxes - Tax Receivable Agreement (Details) - USD ($) $ in Thousands	1 Months Ended		9 Months Ended		12 Months Ended
	Dec. 31, 2023	Aug. 31, 2022	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Dec. 31, 2022
Income Tax Contingency [Line Items]
Percentage of net cash saving to be paid			85.00%		85.00%
Percentage of net cash saving to be retained			15.00%		15.00%
Warrants exercised					$ 250	$ 823
Total TRA liability recognized	$ 5,242		$ 41		5,242	4,333
Outside basis difference in partnership interest					6,200	5,200
Aggregate payment on tax receivable agreement			$ 0	$ 100
Revaluation of tax receivable agreement liability					331
Maximum
Income Tax Contingency [Line Items]
Aggregate payment on tax receivable agreement					$ 100	$ 100
DDM | Class A Common Stock
Income Tax Contingency [Line Items]
Number of units exchanged (in shares)	410,000	100,000			410,000	100,000