Income Taxes - Schedule of Deferred Tax Assets (Liabilities) (Details) - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022
Deferred tax assets:
Net operating loss carryforwards	$ 31,026	$ 44,131
Capital loss carryforwards	8,187	8,187
Federal credit carryforwards	4,487	5,916
Accrued expenses and other reserves	4,620	3,316
Deferred revenue	52,513	33,676
Acquired intangibles	104,634	89,434
Interest limitations carryforward	10,997	10,228
Operating lease liabilities	4,493	4,874
Depreciation	13,152	2,924
Deferred compensation	1,851	1,910
Pension obligation	852	730
Other	4,148	3,078
Total deferred tax assets	240,960	208,404
Valuation allowance for deferred tax assets	(162,966)	(126,860)
Deferred tax assets	77,994	81,544
Deferred tax liabilities:
Depreciation	(5,697)	(6,143)
Acquired intangibles	(11,707)	(14,570)
Convertible debt		(2,463)
Operating lease right-of-use assets	(3,896)	(4,189)
Deferred costs	(8,489)	(2,415)
Other	(2,166)	(749)
Total deferred tax liabilities	(31,955)	(30,529)
Net deferred tax assets	$ 46,039	$ 51,015