Stock-Based Compensation - Employee Stock Purchase Plan (Details) - shares	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares issued under employee stock purchase plan (in shares)	83,715	82,035
Employee Stock
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Purchase price of common stock (as a percent)	85.00%
Shares authorized (in shares)	1,250,000
Shares available for grant (in shares)	586,421