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, 2022	Sep. 30, 2021	Sep. 30, 2020
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Income tax benefit computed at federal statutory rate	$ (2,086)	$ (10,284)	$ (8,461)
State income taxes, net of federal benefit	(776)	(1,005)	(1,557)
Foreign income taxed at different rates	(1,182)	(2,594)	(1,786)
Impact of investments in subsidiaries		7,128	289
Change in deferred tax asset valuation allowance	1,337	(3,247)	(2,514)
Impact of change in uncertain tax positions	(358)	(10,607)	1,144
Global intangible low taxed income, net of foreign tax credits	4,060	4,051	2,815
Impact of tax rate changes	1,531	165	(185)
Compensation	(1,199)	462	(2,302)
Tax credits	(2,102)	(4,050)	(676)
Merger costs	1,629	20	37
Other non-deductible expenses	717	468	398
Other true-ups	763		(520)
Research and development expense deduction	(910)	(730)	(547)
Other	(74)	123	(65)
Income tax benefit	$ 1,350	$ (20,100)	$ (13,930)