Annual report pursuant to Section 13 and 15(d)

Equity-Based Compensation - Additional Information (Details)

v3.22.2.2
Equity-Based Compensation - Additional Information (Details) - Restricted Stock - USD ($)
 12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vested (in shares) (134,481) (207,706) 0  
2019 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Aggregate grant date fair value       $ 3,800,000
2021 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Aggregate grant date fair value   $ 13,600,000    
2022 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Aggregate grant date fair value $ 8,300,000      
Class A Common Stock | 2019 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Options granted (in shares)       292,534
Class A Common Stock | 2021 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Options granted (in shares)   510,733    
Class A Common Stock | 2022 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Options granted (in shares) 256,167      
Class A Common Stock | Non-Employee Directors Under the Equity Incentive Plan | 2019 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Compensation expense $ 400,000 $ 1,300,000 $ 1,600,000  
Unrecognized compensation expense $ 0      
Class A Common Stock | Equity Incentive Plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Options granted (in shares) 256,167      
Class A Common Stock | Equity Incentive Plan | 2021 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Compensation expense $ 3,500,000 $ 2,200,000    
Unrecognized compensation expense $ 7,800,000      
Unrecognized compensation expense, period for recognition (years) 2 years 6 months      
Class A Common Stock | Equity Incentive Plan | 2022 Grants        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Compensation expense $ 3,100,000      
Unrecognized compensation expense $ 5,200,000      
Unrecognized compensation expense, period for recognition (years) 2 years 4 months 24 days