Property and Equipment, net - Accumulated Depreciation and Amortization (Details) - USD ($) $ in Millions	Sep. 30, 2021	Sep. 30, 2020
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 155.3	$ 107.9
Less: accumulated depreciation and amortization	(62.0)	(45.8)
Property and equipment, net	93.3	62.1
Furniture and fixtures
Property, Plant and Equipment [Line Items]
Total property and equipment	15.0	10.2
Software
Property, Plant and Equipment [Line Items]
Total property and equipment	30.0	28.6
Equipment
Property, Plant and Equipment [Line Items]
Total property and equipment	44.1	30.8
Leasehold improvements
Property, Plant and Equipment [Line Items]
Total property and equipment	43.9	38.3
Capitalized software development
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 22.3	$ 0.0