Stock-Based Compensation - Performance-Based Restricted Stock Unit Grants (Details) - Restricted Stock, Performance Based Shares	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Performance-based awards granted, percentage (as a percent)	100.00%	100.00%	100.00%
Performance-based awards granted, percentage, maximum threshold met (as a percent)	200.00%	200.00%	200.00%
Performance goal measurement period (in years)	3 years