Income Taxes - Narrative (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Operating Loss Carryforwards [Line Items]
Income Tax Holiday, Aggregate Dollar Amount	$ 7,200	$ 6,000	$ 8,500
Income Tax Holiday, Income Tax Benefits Per Share	$ 0.12	$ 0.10	$ 0.14
Deferred Tax Assets, Operating Loss Carryforwards	$ 34,787	$ 40,201
Deferred Tax Assets, Tax Credit Carryforwards	25,052	23,883
Valuation Allowance, Deferred Tax Asset, Change in Amount	(4,300)	(2,200)
Unrecognized Tax Benefits	86,877	79,167	$ 66,840	$ 70,814
Unrecognized Tax Benefits that Would Impact Effective Tax Rate	56,200	51,200	43,200
Unrecognized Tax Benefits, Period Increase (Decrease)	5,600	3,300	$ (1,500)
Unrecognized Tax Benefits, Income Tax Penalties and Interest Accrued	11,800	$ 6,200
Foreign [Member]
Operating Loss Carryforwards [Line Items]
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration	54,900
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration	200
Deferred Tax Assets, Tax Credit Carryforwards	400
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration	2,600
Domestic Tax Jurisdiction [Member]
Operating Loss Carryforwards [Line Items]
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration	53,300
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration	16,200
Deferred Tax Assets, Operating Loss Carryforwards	69,500
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration	3,500
State and Local Jurisdiction [Member]
Operating Loss Carryforwards [Line Items]
Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration	45,500
Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration	153,800
Deferred Tax Assets, Operating Loss Carryforwards	199,300
Deferred Tax Assets, Tax Credit Carryforwards	33,900
Deferred Tax Assets, Tax Credit Carryforwards, Subject to Expiration	$ 3,400