Related Party Transactions (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Related Party Transaction [Line Items]
Selling, general and administrative expenses	$ 216.3	$ 189.7	$ 167.1
Reimbursable start up costs	2.5
Cash distribution directly to related party		3.2	20.4
Cash distribution on behalf of related party to third party		0.0	4.2
Master services agreement fees
Related Party Transaction [Line Items]
Selling, general and administrative expenses	$ 4.0	$ 4.6	$ 2.2