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Stockholders' and Members' Equity, Equity-Based Compensation (Details)
$ / shares in Units, $ in Millions
3 Months Ended 9 Months Ended
Apr. 20, 2023
shares
Oct. 01, 2022
shares
Sep. 30, 2022
shares
Jun. 30, 2022
USD ($)
$ / shares
shares
Jun. 30, 2021
USD ($)
Jun. 30, 2022
USD ($)
Intallment
$ / shares
shares
Jun. 30, 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)               1,556,307
Restricted Stock Units (RSUs) [Member]                
Equity-Based Compensation [Abstract]                
Compensation expense | $       $ 2.5 $ 1.1 $ 7.3 $ 3.3  
Number of Shares [Abstract]                
Beginning balance (in shares)           545,094    
Awarded (in shares)           173,697    
Vested (in shares)           (100,872)    
Forfeited (in shares)           0    
Ending balance (in shares)       617,919   617,919    
Weighted Average Grant Date Fair Value [Abstract]                
Beginning balance (in dollars per share) | $ / shares           $ 22.68    
Awarded (in dollars per share) | $ / shares           39.95    
Vested (in dollars per share) | $ / shares           16.99    
Forfeited (in dollars per share) | $ / shares           0    
Ending balance (in dollars per share) | $ / shares       $ 28.46   $ 28.46    
Unrecognized compensation expense | $       $ 8.8   $ 8.8    
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)           121,470    
Time-Based Restricted Stock Units [Member] | Plan [Member]                
Number of Shares [Abstract]                
Awarded (in shares) 12,000 14,186 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 | $       $ 1.3 $ 0.6 $ 4.0 $ 1.3  
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%