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Stockholders' Equity, Equity-Based Compensation (Details)
$ / shares in Units, $ in Millions
8 Months Ended 12 Months Ended
Oct. 01, 2021
$ / shares
shares
Feb. 07, 2021
shares
Sep. 30, 2020
$ / shares
shares
Sep. 30, 2021
USD ($)
Intallment
$ / shares
shares
Sep. 30, 2020
USD ($)
Intallment
$ / shares
shares
Feb. 11, 2020
shares
Weighted Average Grant Date Fair Value [Abstract]            
Compensation expense | $       $ 5.7 $ 1.6  
Class A Common Stock [Member]            
Equity-Based Compensation [Abstract]            
Total number of shares reserved for issuance (in shares)           1,509,565
Restricted Stock Units (RSUs) [Member]            
Equity-Based Compensation [Abstract]            
Awarded (in shares)     256,977 348,927    
Number of Shares [Abstract]            
Beginning balance (in shares) 545,094   44,666 301,643    
Awarded (in shares)     256,977 348,927    
Vested (in shares)     0 (105,476)    
Forfeited (in shares)     0 0    
Ending balance (in shares)     301,643 545,094 301,643  
Weighted Average Grant Date Fair Value [Abstract]            
Beginning balance (in dollars per share) | $ / shares $ 22.68   $ 14.61 $ 15.78    
Awarded (in dollars per share) | $ / shares     15.98 27.37    
Vested (in dollars per share) | $ / shares     0 18.47    
Forfeited (in dollars per share) | $ / shares     0 0    
Ending balance (in dollars per share) | $ / shares     $ 15.78 $ 22.68 $ 15.78  
Unrecognized compensation expense | $       $ 7.0    
Weighted-average period of recognition       1 year 6 months    
Performance Share Unit [Member]            
Weighted Average Grant Date Fair Value [Abstract]            
Compensation expense | $       $ 2.6 $ 0.5  
2021 Awards [Member] | Time-Based Restricted Stock Units [Member]            
Equity-Based Compensation [Abstract]            
Number of equal annual installments for vesting | Intallment       4    
Awarded (in shares) 25,620     143,947    
Number of Shares [Abstract]            
Awarded (in shares) 25,620     143,947    
2021 Awards [Member] | Time-Based Restricted Stock Units [Member] | Plan [Member]            
Equity-Based Compensation [Abstract]            
Awarded (in shares) 118,327          
Number of Shares [Abstract]            
Awarded (in shares) 118,327          
2021 Awards [Member] | Performance Share Unit [Member]            
Equity-Based Compensation [Abstract]            
Number of equal annual installments for vesting | Intallment       3    
Awarded (in shares)       102,490    
Percentage of target award granted       100.00%    
Number of shares of common stock consisted in each unit (in shares)       1    
Percentage of expected performance targets to be achieved target award       200.00%    
Number of Shares [Abstract]            
Awarded (in shares)       102,490    
2021 Awards [Member] | Performance Share Unit [Member] | Minimum [Member]            
Equity-Based Compensation [Abstract]            
Percentage of actual number of unit earned       0.00%    
2021 Awards [Member] | Performance Share Unit [Member] | Maximum [Member]            
Equity-Based Compensation [Abstract]            
Percentage of actual number of unit earned       200.00%    
2020 Awards [Member]            
Equity-Based Compensation [Abstract]            
Awarded (in shares)       44,666    
Percentage of expected performance targets to be achieved target award       175.00%    
Number of Shares [Abstract]            
Awarded (in shares)       44,666    
2020 Awards [Member] | Restricted Stock Units (RSUs) [Member]            
Equity-Based Compensation [Abstract]            
Number of equal annual installments for vesting | Intallment         4  
Awarded (in shares)   39,727     100,000  
Number of Shares [Abstract]            
Awarded (in shares)   39,727     100,000  
2020 Awards [Member] | Restricted Stock Units (RSUs) [Member] | Board of Directors [Member]            
Equity-Based Compensation [Abstract]            
Number of equal annual installments for vesting | Intallment         4  
Awarded (in shares)         139,727  
Number of Shares [Abstract]            
Awarded (in shares)         139,727  
2020 Awards [Member] | Performance Share Unit [Member]            
Equity-Based Compensation [Abstract]            
Number of equal annual installments for vesting | Intallment       3    
Awarded (in shares)       67,000    
Percentage of target award granted       100.00%    
Number of shares of common stock consisted in each unit (in shares)       1    
Award vesting period       3 years    
Number of Shares [Abstract]            
Awarded (in shares)       67,000    
2020 Awards [Member] | Performance Share Unit [Member] | Minimum [Member]            
Equity-Based Compensation [Abstract]            
Percentage of actual number of unit earned       0.00%    
2020 Awards [Member] | Performance Share Unit [Member] | Maximum [Member]            
Equity-Based Compensation [Abstract]            
Percentage of actual number of unit earned       175.00%