Intangible Assets, net (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
	Mar. 31, 2024	Mar. 31, 2024	Sep. 30, 2023
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	$ 328.3	$ 328.3	$ 375.5
Finite-lived intangible assets, accumulated amortization	(177.9)	(177.9)	(198.7)
Finite-lived intangible assets, net	150.4	150.4	176.8
Accelerated amortization	17.4	17.4
Customer relationships
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	160.7	160.7	178.4
Finite-lived intangible assets, accumulated amortization	(90.2)	(90.2)	(97.2)
Finite-lived intangible assets, net	70.5	70.5	81.2
Trademarks and brands
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	164.5	164.5	194.0
Finite-lived intangible assets, accumulated amortization	(84.6)	(84.6)	(98.4)
Finite-lived intangible assets, net	79.9	79.9	95.6
Other intangible assets
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	3.1	3.1	3.1
Finite-lived intangible assets, accumulated amortization	(3.1)	(3.1)	(3.1)
Finite-lived intangible assets, net	$ 0.0	$ 0.0	$ 0.0