CONSOLIDATED STATEMENTS OF STOCKHOLDERS’ EQUITY - USD ($) $ in Thousands	Total	Class A Common Stock	Class B Common Stock	Common Stock Class A Common Stock	Common Stock Class B Common Stock	Additional Paid-in Capital	Retained Earnings	Non- controlling Interest	Accumulated Other Comprehensive Income (Loss)
Beginning balance (in shares) at Sep. 30, 2021				13,277,000	1,819,000
Beginning balance at Sep. 30, 2021	$ 254,833			$ 133	$ 18	$ 150,825	$ 74,952	$ 28,905	$ 0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income	152,611						130,944	21,667
Distributions to members	(4,281)						(784)	(3,497)
Exchange of B shares for A shares (in shares)				389,000	(389,000)
Exchange of B shares for A shares	0			$ 4	$ (4)	6,833		(6,833)
Establishment of liabilities under tax receivable agreement and related changes to deferred tax assets associated with increase in tax basis	(247)					(247)
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)				169,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(1,628)			$ 1		(1,629)
Shares issued in connection with business combinations	14,627			$ 4		14,623
Non-controlling interest in subsidiary	19,311							19,311
Equity-based compensation	10,013					10,013
Repurchase and retirement of Class A common stock (in shares)				(10,000)
Repurchase and retirement of Class A common stock	(354)					(122)	(232)
Currency translation adjustment	(8)							(1)	(7)
Ending balance (in shares) at Sep. 30, 2022				14,212,000	1,430,000
Ending balance at Sep. 30, 2022	444,877			$ 142	$ 14	180,296	204,880	59,552	(7)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Shares issued in connection with a business combination (in shares)				387,000
Net (loss) income	(39,111)						(38,592)	(519)
Distributions to members	(3,603)						(38)	(3,565)
Establishment of liabilities under tax receivable agreement and related changes to deferred tax assets associated with increase in tax basis	4,402					4,402
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)				186,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(1,971)			$ 2		(1,973)
Shares issued as part of employee stock purchase plan (in shares)				86,000
Shares issued as part of employee stock purchase plan	2,092			$ 1		2,091
Equity-based compensation	8,962					8,962
Repurchase and retirement of Class A common stock (in shares)				(64,000)
Repurchase and retirement of Class A common stock	(1,579)			$ (1)		(760)	(818)
Currency translation adjustment	9							1	8
Ending balance (in shares) at Sep. 30, 2023		14,420,129	1,429,940	14,420,000	1,430,000
Ending balance at Sep. 30, 2023	414,078			$ 144	$ 14	193,018	165,432	55,469	1
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net (loss) income	(6,176)						(5,705)	(471)
Distributions to members	(5,415)						(102)	(5,313)
Establishment of liabilities under tax receivable agreement and related changes to deferred tax assets associated with increase in tax basis	1,868					1,868
Shares issued upon vesting of equity-based awards, net of tax withholding (in shares)				208,000
Shares issued upon vesting of equity-based awards, net of tax withholding	(2,641)			$ 2		(2,643)
Shares issued as part of employee stock purchase plan (in shares)				59,000
Shares issued as part of employee stock purchase plan	1,520			$ 1		1,519
Equity-based compensation	8,443					8,443
Repurchase and retirement of Class A common stock (in shares)		0
Currency translation adjustment	(18)							(2)	(16)
Change in fair value of cash flow swaps	(2,066)							(184)	(1,882)
Ending balance (in shares) at Sep. 30, 2024		14,686,696	1,429,940	14,687,000	1,430,000
Ending balance at Sep. 30, 2024	390,753			$ 147	$ 14	202,921	$ 159,625	29,943	$ (1,897)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Purchase of non-controlling interest	$ (18,840)					$ 716		$ (19,556)