Stock-Based Compensation - Schedule of Stock-Based Compensation Expense (Income) (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2022	Sep. 30, 2021	Sep. 30, 2020
Equity-based compensation plans
Stock-based compensation expense	$ 4.9	$ 28.7	$ 29.8	$ 30.2
Income tax benefit recognized for stock-based compensation	(0.8)	(4.2)	(4.4)	(3.6)
Stock-based compensation cost, net of tax	4.1	24.5	25.4	26.6
Stock options
Equity-based compensation plans
Stock-based compensation expense	0.2	0.3	1.8	6.8
Nonvested Stock Awards [Member]
Equity-based compensation plans
Stock-based compensation expense	3.5	25.7	19.3	15.8
Income tax benefit recognized for stock-based compensation	3.1	2.5	2.0	3.1
Performance Shares [Member]
Equity-based compensation plans
Stock-based compensation expense	0.5	2.6	6.1	6.7
Stock Appreciation Rights (SARs)
Equity-based compensation plans
Stock-based compensation expense	0.3	(0.8)	1.1	0.2
Restricted Stock Units (RSUs)
Equity-based compensation plans
Stock-based compensation expense	$ 0.4	$ 0.9	$ 1.5	$ 0.7