Leases - Operating Lease Costs and Other Related Information (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
Leases [Abstract]
Operating lease costs	$ 28.0	$ 25.7
Cash paid for amounts included in the measurement of operating lease liabilities	18.4	16.4
Right-of-use assets obtained in exchange for operating lease liabilities	$ 14.3	$ 12.4
Weighted average remaining lease term (years)	9 years 9 months 18 days	10 years 10 months 24 days
Weighted average discount rate	4.50%	4.30%