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Equity-Based Compensation - Additional Information (Details) - USD ($)
$ / shares in Units, $ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
May 31, 2021
Sep. 30, 2020
May 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Income tax benefits related to equity-based compensation $ 785 $ 468 $ 1,083      
Granted, weighted average grant date fair value (in USD per share) $ 13.68          
Stock options outstanding (in shares) 8,576,670 8,222,322        
Options exercisable at end of period (in shares) 5,586,736          
Unrecognized compensation expense related to unvested options at end of period $ 23,395          
Period for recognition of unrecognized compensation cost 2 years 1 month 6 days          
Fair value of stock options that vested $ 24,652          
Restricted stock units            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Period for recognition of unrecognized compensation cost 3 years 1 month 6 days          
Granted, weighted average exercise price (in USD per share) $ 25.28          
Cost not yet recognized, amount $ 12,126          
2018 Equity Incentive Award Plan            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Shares available for grant under the plan (in shares) 1,075,549         3,500,000
Additional Class A common shares added at the beginning of calendar year as percentage of common stock outstanding at end of previous year           4.00%
2020 Equity Incentive Award Plan            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Shares available for grant under the plan (in shares) 1,154,571     3,000,000 1,500,000