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Equity-Based Compensation - Summary of Company's Stock Options Activity (Details)
9 Months Ended
Jun. 30, 2025
$ / shares
shares
Share-Based Payment Arrangement [Abstract]  
Outstanding at September 30, 2024 | shares 3,036,000
Exercised | shares 128,000
Forfeited | shares 531,000
Outstanding at June 30, 2025 | shares 2,377,000
Stock option vested and exercisable upon issuance | shares 2,063,000
Expected to vest after June 30, 2025 | shares 314,000
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]  
Weighted Average Exercise Price, Outstanding at September 30, 2024 | $ / shares $ 19.37
Exercised, weighted average exercise price | $ / shares 14.09
Forfeited, weighted average exercise price | $ / shares 21.7
Weighted Average Exercise Price, Outstanding at June 30, 2025 | $ / shares 19.13
Weighted Average Exercise Price, Vested and Exercisable at June 30, 2025 | $ / shares 18.93
Weighted Average Exercise Price, Expected to vest after June 30, 2025 | $ / shares $ 20.46