Significant Accounting Policies - Schedule of Disaggregation of Sales by Timing of Revenue Recognized (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Revenue from External Customer [Line Items]
Net revenues	$ 1,619.0	$ 1,443.5	$ 1,236.1
Franchise fees and other
Revenue from External Customer [Line Items]
Net revenues	80.2	71.6	74.4
Transferred at Point in Time
Revenue from External Customer [Line Items]
Net revenues	1,543.0	1,375.0	1,177.2
Transferred over Time | Franchise fees and other
Revenue from External Customer [Line Items]
Net revenues	$ 76.0	$ 68.5	$ 58.9