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, 2021	Sep. 30, 2020	Sep. 30, 2019
Effective Income Tax Rate Reconciliation, Amount [Abstract]
Income tax benefit computed at federal statutory rate	$ (10,284)	$ (8,461)	$ (17,631)
State income taxes, net of federal benefit	(1,005)	(1,557)	(3,856)
Foreign income taxed at different rates	(2,594)	(1,786)	(1,408)
Impact of investments in subsidiaries	7,128	289	(536)
Change in deferred tax asset valuation allowance	(3,247)	(2,514)	(1,834)
Impact of change in uncertain tax positions	(10,607)	1,144	720
Global intangible low taxed income, net of foreign tax credits	4,051	2,815	393
Impact of tax rate change	165	(185)	(1,440)
Compensation	462	(2,302)	(165)
Tax credits	(4,050)	(676)	(689)
Merger costs	20	37	593
Other taxes	468	398	432
Transition tax and other true-ups		(520)	2,909
Research and development expense deduction	(730)	(547)	(447)
Other	123	(65)	129
Income tax benefit	$ (20,100)	$ (13,930)	$ (22,830)