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Stockholders' and Members' Equity, Equity-Based Compensation (Details)
$ / shares in Units, $ in Millions
3 Months Ended 6 Months Ended
Oct. 01, 2022
shares
Sep. 30, 2022
shares
Mar. 31, 2022
USD ($)
$ / shares
shares
Mar. 31, 2021
USD ($)
Mar. 31, 2022
USD ($)
Intallment
$ / shares
shares
Mar. 31, 2021
USD ($)
Feb. 11, 2020
shares
Equity-Based Compensation [Abstract]              
Percentage of expected performance targets to be achieved target award     200.00%   200.00%    
Class A Common Stock [Member]              
Equity-Based Compensation [Abstract]              
Total number of shares reserved for issuance (in shares)             1,530,923
Restricted Stock Units (RSUs) [Member]              
Equity-Based Compensation [Abstract]              
Compensation expense | $     $ 2.7 $ 1.1 $ 4.8 $ 2.2  
Number of Shares [Abstract]              
Beginning balance (in shares)         545,094    
Awarded (in shares)         160,573    
Vested (in shares)         (100,872)    
Forfeited (in shares)         0    
Ending balance (in shares)     604,795   604,795    
Weighted Average Grant Date Fair Value [Abstract]              
Beginning balance (in dollars per share) | $ / shares         $ 22.68    
Awarded (in dollars per share) | $ / shares         40.44    
Vested (in dollars per share) | $ / shares         16.99    
Forfeited (in dollars per share) | $ / shares         0    
Ending balance (in dollars per share) | $ / shares     $ 28.34   $ 28.34    
Unrecognized compensation expense | $     $ 10.8   $ 10.8    
Weighted-average period of recognition         1 year 4 months 24 days    
Time-Based Restricted Stock Units [Member]              
Equity-Based Compensation [Abstract]              
Number of equal annual installments for vesting | Intallment         3    
Number of Shares [Abstract]              
Awarded (in shares)         108,346    
Time-Based Restricted Stock Units [Member] | Plan [Member]              
Number of Shares [Abstract]              
Awarded (in shares) 13,062 95,284          
Performance Share Unit [Member]              
Equity-Based Compensation [Abstract]              
Percentage of target award granted         100.00%    
Number of equal annual installments for vesting | Intallment         3    
Number of shares of common stock consisted in each unit (in shares)         1    
Compensation expense | $     $ 1.7 $ 0.4 $ 2.7 $ 0.7  
Number of Shares [Abstract]              
Awarded (in shares)         52,227    
Performance Share Unit [Member] | Minimum [Member]              
Equity-Based Compensation [Abstract]              
Percentage of actual number of unit earned         0.00%    
Performance Share Unit [Member] | Maximum [Member]              
Equity-Based Compensation [Abstract]              
Percentage of actual number of unit earned         200.00%