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Equity-Based Compensation - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions					12 Months Ended
	Nov. 17, 2023	Nov. 14, 2022	May 17, 2022	Nov. 15, 2021	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Sep. 11, 2023	Mar. 10, 2020	Oct. 22, 2018
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares exercised					166,000
Equity-based compensation					$ 20.2	$ 22.1	$ 18.9
Unrecognized compensation cost					$ 30.6	$ 23.7	$ 36.2
Unamortized value of outstanding stock-based compensation, weighted average remaining life					1 year 2 months 12 days	1 year 2 months 12 days	1 year 2 months 12 days
Amended and Restated 2018 Omnibus Incentive Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares of common stock that may be issued									24,650,000
2023 Employment Inducement Incentive Award Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Number of shares of common stock that may be issued								1,750,000
ESPP
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Common stock shares available for sale										2,100,000
Common stock shares issued	188,000	177,000		112,000
Restricted Stock Units (RSU) [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Vesting period					4 years
Non-cash equity-based compensation expense over the requisite service period					$ 19.2
Stock options weighted average grant date fair value					$ 8.24
Number of shares exercised					1,285,000
Performance stock unit awards vested					1,285,000
RSUs Forfeited					689,000
Common stock shares issued					2,667,000
Performance stock units issued					2,667,000
Weighted average distribution price per share of PSU					$ 8.24
Employee Stock Option
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Non-cash equity-based compensation expense over the requisite service period					$ 6.3
Performance Shares
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Weighted average exercise price					$ 7.35
Performance stock unit awards vested					0
RSUs Forfeited					316,000
Performance stock units issued					918,000
Weighted average distribution price per share of PSU					$ 7.35
Performance Shares \| Minimum
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Performance Stock unit awards vesting rights percentage			0.00%
Performance Shares \| Maximum
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Performance Stock unit awards vesting rights percentage			200.00%