Intangible Assets - Gross and Net Intangible Assets by Major Class (Details) - USD ($) $ in Millions	Sep. 30, 2023	Sep. 30, 2022
Acquired Finite-Lived Intangible Assets [Line Items]
Finite-lived intangible assets, gross amount	$ 70.9	$ 61.5
Finite-lived intangible assets, accumulated amortization	(53.4)	(39.0)
Finite-lived intangible assets, net amount	17.5	22.5
Indefinite-lived intangible assets	5.6	5.5
Intangible assets, gross amount	76.5	67.0
Total intangible assets, net amount	23.1	28.0
Website domains
Acquired Finite-Lived Intangible Assets [Line Items]
Indefinite-lived intangible assets	1.9	1.8
Business licenses
Acquired Finite-Lived Intangible Assets [Line Items]
Indefinite-lived intangible assets	3.7	3.7
Trade/domain names
Acquired Finite-Lived Intangible Assets [Line Items]
Finite-lived trade/domain names, gross amount	4.1	3.7
Finite-lived intangible assets, accumulated amortization	(2.4)	(1.6)
Finite-lived intangible assets, net amount	1.7	2.1
Software programs/platforms
Acquired Finite-Lived Intangible Assets [Line Items]
Finite-lived software programs/platforms, gross amount	28.5	28.3
Finite-lived intangible assets, accumulated amortization	(26.9)	(19.4)
Finite-lived intangible assets, net amount	1.6	8.9
Client base
Acquired Finite-Lived Intangible Assets [Line Items]
Finite-lived customer base, gross amount	38.3	29.5
Finite-lived intangible assets, accumulated amortization	(24.1)	(18.0)
Finite-lived intangible assets, net amount	$ 14.2	$ 11.5