Stock-Based Compensation - Stock-Based Compensation Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation	$ 9,376	$ 12,443	$ 20,051
Income tax benefit	(1,406)	(1,929)	(3,208)
Total compensation expense included in the statement of operations	7,970	10,514	16,843
Restricted Stock Units (RSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation	8,027	10,597	18,923
Employee Stock
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation	$ 1,349	$ 1,846	$ 1,128