Property and Equipment, net - Accumulated Depreciation and Amortization (Details) - USD ($) $ in Millions	Sep. 30, 2022	Sep. 30, 2021
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 186.1	$ 155.3
Less: accumulated depreciation and amortization	(73.2)	(62.0)
Property and equipment, net	112.9	93.3
Furniture and fixtures
Property, Plant and Equipment [Line Items]
Total property and equipment	16.0	15.0
Software
Property, Plant and Equipment [Line Items]
Total property and equipment	34.4	30.0
Equipment
Property, Plant and Equipment [Line Items]
Total property and equipment	45.3	44.1
Leasehold improvements
Property, Plant and Equipment [Line Items]
Total property and equipment	43.3	43.9
Capitalized software development
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 47.1	$ 22.3