Income Taxes - Differences Between Income Tax Provision (Benefit) and Income Taxes Computed using Applicable U.S. Statutory Federal Tax Rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Income tax benefit computed at federal statutory rate	$ (6,331)	$ (2,086)	$ (10,284)
State income taxes, net of federal benefit	(851)	(776)	(1,005)
Foreign income taxed at different rates	(22)	(1,182)	(2,594)
Impact of investments in subsidiaries	(6,058)		7,128
Nontaxable gain from acquisition earn-out liability reversal	(3,959)
Change in deferred tax asset valuation allowance	1,137	1,337	(3,247)
Impact of change in uncertain tax positions	(1,321)	(358)	(10,607)
Global intangible low taxed income, net of foreign tax credits		4,060	4,051
Impact of tax rate changes	(1,391)	1,531	165
Compensation	1,598	(1,199)	462
Tax credits	(1,434)	(2,102)	(4,050)
Merger costs	1,056	1,629	20
Other non-deductible expenses and other taxes	1,304	643	591
Impact of effective state tax rate change		763
Research and development expense deduction	(1,278)	(910)	(730)
Income tax (benefit) expense	$ (17,550)	$ 1,350	$ (20,100)