Stock-Based Compensation - Restricted Stock Unit Activity - Additional Information (Details) - Restricted Stock Units (RSUs) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Fair value of restricted stock awards vested	$ 14.8	$ 66.9	$ 28.4
Withholding taxes remitted	$ 5.0	$ 25.2	$ 9.8
Restricted stocks granted (in shares)	590,066	249,685	349,930
Discontinued Operations, Held-for-sale or Disposed of by Sale
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Restricted stocks granted (in shares)	0		98,783