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Summary of Significant Accounting Policies - Other Intangible Assets (Details) - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Finite-Lived and Indefinite-Lived, Intangible Assets      
Amortization of intangible assets $ 184.6 $ 160.7 $ 146.0
Finite-Lived Intangible Assets, Future Amortization Expense [Abstract]      
2025 184.8    
2026 184.8    
2027 184.8    
2028 179.7    
2029 168.7    
Finite-Lived Intangible Assets [Abstract]      
Finite-Lived Intangible Assets, Gross 3,521.6 3,421.3  
Finite-Lived Intangible Assets, Accumulated Amortization (1,432.5) (1,242.0)  
Finite-Lived Intangible Assets, Net 2,089.1 2,179.3  
Intangible Assets, Net (Excluding Goodwill) [Abstract]      
Carrying amount, total 4,578.5 4,454.4  
Other intangible assets, net 3,146.0 3,212.4  
Customer Relationships      
Finite-Lived Intangible Assets [Abstract]      
Finite-Lived Intangible Assets, Gross 2,633.3 2,535.5  
Finite-Lived Intangible Assets, Accumulated Amortization (1,084.1) (940.7)  
Finite-Lived Intangible Assets, Net 1,549.2 1,594.8  
Trademarks      
Finite-Lived Intangible Assets [Abstract]      
Finite-Lived Intangible Assets, Gross 888.3 885.8  
Finite-Lived Intangible Assets, Accumulated Amortization (348.4) (301.3)  
Finite-Lived Intangible Assets, Net 539.9 584.5  
Trademarks      
Indefinite-lived Intangible Assets (Excluding Goodwill) [Abstract]      
Indefinite-lived Intangible Assets (Excluding Goodwill) $ 1,056.9 $ 1,033.1  
Intangible Assets, Net (Excluding Goodwill) [Abstract]      
Reporting Unit, Percentage of Fair Value in Excess of Carrying Amount 9.00% 11.00%