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Share-Based Compensation - Schedule of Stock Option Activity (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Number of Options Outstanding      
Number of options outstanding, beginning (in shares) 4,591,552    
Number of options outstanding, granted (in shares) 533,127    
Number of options outstanding, exercised (in shares) (407,084)    
Number of options outstanding, forfeited (in shares) (55,993)    
Number of options outstanding, expired (in shares) (851)    
Number of options outstanding, ending (in shares) 4,660,751 4,591,552  
Number of options outstanding, exercisable (in shares) 1,234,595    
Weighted Average  Exercise Price      
Weighted average exercise price, beginning (in dollar per share) $ 34.42    
Weighted average  exercise price, granted (in dollar per share) 77.18    
Weighted average  exercise price, exercised (in dollar per share) 26.26    
Weighted average  exercise price, forfeited (in dollar per share) 39.62    
Weighted average  exercise price, expired (in dollar per share) 27.60    
Weighted average exercise price, ending (in dollar per share) 39.97 $ 34.42  
Weighted average  exercise price, exercisable (in dollar per share) 23.47    
Weighted Average Grant Date Fair Value      
Weighted average grant date fair value, beginning (in dollar per share) 12.86    
Weighted average grant date fair value, granted (in dollar per share) 27.93 26.77 $ 22.14
Weighted average grant date fair value, exercised (in dollar per share) 8.43    
Weighted average grant date fair value, forfeited (in dollar per share) 13.39    
Weighted average grant date fair value, expired (in dollar per share) 10.84    
Weighted average grant date fair value, ending (in dollar per share) 14.96 $ 12.86  
Weighted average grant date fair value, exercisable (in dollar per share) $ 6.83    
Stock Option Activity, Additional Disclosures      
Weighted average remaining term 4 years 5 months 19 days 5 years 21 days  
Weighted average remaining term, exercisable 1 year 9 months 14 days    
Aggregate intrinsic value $ 284.1 $ 88.7  
Aggregate intrinsic value, exercisable $ 95.6