Equity-Based Compensation - Schedule of Weighted-Average Assumptions Used in Valuation of Unit Awards, Restricted Stock Unit Awards Were Converted and Stock Option Awards Granted or Modified (Details)	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]
Risk-free interest rate	0.49%	1.56%	2.85%
Dividend yield	0.00%	0.00%	0.00%
Volatility factor	54.40%	43.51%	38.85%
Expected term (in years)	6 years 4 months 24 days	6 years 3 months 18 days	6 years 3 months 18 days