Property and Equipment, net - Property and Equipment at cost less Accumulated Depreciation and Amortization (Details) - USD ($) $ in Millions	Sep. 30, 2023	Sep. 30, 2022
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 230.2	$ 186.1
Less: accumulated depreciation and amortization	(106.7)	(73.2)
Property and equipment, net	123.5	112.9
Furniture and fixtures
Property, Plant and Equipment [Line Items]
Total property and equipment	17.5	16.0
Software
Property, Plant and Equipment [Line Items]
Total property and equipment	38.1	34.4
Equipment
Property, Plant and Equipment [Line Items]
Total property and equipment	49.9	45.3
Leasehold improvements
Property, Plant and Equipment [Line Items]
Total property and equipment	47.7	43.3
Capitalized software development
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 77.0	$ 47.1