Income Taxes - Schedule of Deferred Tax Assets (Liabilities) (Details) - USD ($) $ in Thousands	Sep. 30, 2024	Sep. 30, 2023
Deferred tax assets:
Net operating loss carryforwards	$ 40,155	$ 31,026
Capital loss carryforwards		8,187
Federal credit carryforwards	7,380	4,487
Accrued expenses and other reserves	3,119	4,620
Deferred revenue	37,508	52,513
Acquired intangibles	110,844	104,634
Interest limitations carryforward	9,456	10,997
Operating lease liabilities	3,714	4,493
Depreciation	25,394	13,152
Deferred compensation	1,028	1,851
Pension obligation	462	852
Other	3,873	4,148
Total deferred tax assets	242,933	240,960
Valuation allowance for deferred tax assets	(167,314)	(162,966)
Deferred tax assets	75,619	77,994
Deferred tax liabilities:
Depreciation	(5,006)	(5,697)
Acquired intangibles	(6,889)	(11,707)
Operating lease right-of-use assets	(3,557)	(3,896)
Deferred costs	(7,691)	(8,489)
Other	(1,656)	(2,166)
Total deferred tax liabilities	(24,799)	(31,955)
Net deferred tax assets	$ 50,820	$ 46,039