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Equity and Stock-Based Compensation - Stock Options - Additional Information (Details) - USD ($)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Intrinsic value of options outstanding	$ 3,012,000
Intrinsic value of options exercisable	$ 1,844,000
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock price	$ 11.43
Intrinsic value of stock options exercised	$ 800,000	$ 100,000	$ 100,000
Stock Options \| Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Option vesting period	6 months
Stock Options \| Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expiration period	10 years
Option vesting period	4 years