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Share-Based Payments - Narrative (Details) - USD ($)
shares in Millions, $ in Millions
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]      
Compensation expense under defined contribution plans $ 26.0 $ 24.7 $ 23.1
Compensation expense related to share-based payments 61.4 61.5 $ 45.9
Unrecognized compensation expense $ 106.7 $ 68.7  
Recognition period of unrecognized compensation expense (in years) 3 years 3 years  
Performance Shares      
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]      
Vesting period (in years) 3 years    
2020 Stock Incentive Plan      
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]      
Securities available for future issuance (in shares) 11.3    
2020 Stock Incentive Plan | Employee Stock Option      
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]      
Expiration term of unexercised options (in years) 7 years