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Goodwill and Other Intangible Assets - Schedule of Definite-Lived Intangible Assets (Details) - USD ($)
$ in Millions
Sep. 30, 2025
Sep. 30, 2024
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value $ 1,541.5 $ 2,141.0
Accumulated Amortization (775.8) (1,190.4)
Total 765.7 950.6
Management contracts [Member]    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 1,255.3 1,758.8
Accumulated Amortization (709.3) (1,061.8)
Total 546.0 697.0
Trade Names [Member]    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 286.2 367.8
Accumulated Amortization (66.5) (115.9)
Total 219.7 251.9
Developed software [Member]    
Finite-Lived Intangible Assets [Line Items]    
Gross Carrying Value 0.0 14.4
Accumulated Amortization 0.0 (12.7)
Total $ 0.0 $ 1.7