Intangible Assets, net (Details) - USD ($) $ in Millions	Jun. 30, 2023	Sep. 30, 2022
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	$ 375.5	$ 376.5
Finite-lived intangible assets, accumulated amortization	(186.7)	(173.2)
Finite-lived intangible assets, net	188.8	203.3
Customer relationships
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	178.4	178.3
Finite-lived intangible assets, accumulated amortization	(92.3)	(84.9)
Finite-lived intangible assets, net	86.1	93.4
Trademarks and brands
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	194.0	195.1
Finite-lived intangible assets, accumulated amortization	(91.3)	(85.2)
Finite-lived intangible assets, net	102.7	109.9
Other intangible assets
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	3.1	3.1
Finite-lived intangible assets, accumulated amortization	(3.1)	(3.1)
Finite-lived intangible assets, net	$ 0.0	$ 0.0