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Stock-Based Compensation - Schedule of Assumptions for Stock Options Granted (Details) - Stock options - $ / shares
12 Months Ended
Sep. 30, 2022
Sep. 30, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Expected life of options (in years) 5 years 8 months 12 days 5 years 8 months 12 days
Expected volatility (percentage) 55.02% 51.52%
Expected dividends 0.00% 0.00%
Weighted-average risk-free interest rate 1.88% 0.43%
Weighted average fair value (in dollars per share) $ 8.54 $ 4.99