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Significant Accounting Policies - Schedule of Sales Disaggregated by Segment and Geographical Area (Details) - USD ($)
$ in Millions
 12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Disaggregation of Revenue [Line Items]      
Net revenues $ 1,710.3 $ 1,619.0 $ 1,443.5
Discontinued Operations, Held-for-sale      
Disaggregation of Revenue [Line Items]      
Net revenues associated with suspended operations 0.0 0.0 1,174.4
Franchise fees and other      
Disaggregation of Revenue [Line Items]      
Net revenues 94.6 80.2 71.6
Franchise fees and other | Discontinued Operations, Held-for-sale      
Disaggregation of Revenue [Line Items]      
Net revenues associated with suspended operations     0.2
United States      
Disaggregation of Revenue [Line Items]      
Net revenues 1,657.1 1,571.8 1,407.7
Non-U.S.      
Disaggregation of Revenue [Line Items]      
Net revenues $ 53.2 $ 47.2 $ 35.8