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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Jun. 30, 2025
Jun. 30, 2024
Jun. 30, 2025
Jun. 30, 2024
Sep. 30, 2024
Operating Loss Carryforwards [Line Items]          
Effective income tax rate reconciliation (in percent) 24.70% 27.50% 36.80% 34.40%  
Tax receivable agreement liability $ 40.8   $ 40.8   $ 40.6
Percentage of net cash savings     85.00%    
Deferred Tax Assets, Operating Loss Carryforwards, Domestic         0.9
Tax Credit Carryforward, Amount         3.7
Deferred Tax Asset, Interest Carryforward         0.9
Domestic Tax Jurisdiction          
Operating Loss Carryforwards [Line Items]          
Operating loss carryforwards         4.3
State and Local Jurisdiction          
Operating Loss Carryforwards [Line Items]          
Operating loss carryforwards         $ 0.3