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, 2022	Sep. 30, 2021	Sep. 30, 2020
Share-Based Payment Arrangement [Abstract]
Risk-free interest rate	1.88%	0.49%	1.56%
Dividend yield	0.00%	0.00%	0.00%
Volatility factor	47.10%	54.40%	43.51%
Expected term (in years)	5 years 3 months 18 days	6 years 4 months 24 days	6 years 3 months 18 days