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, 2024
Share-Based Payment Arrangement [Abstract]
Risk-free interest rate	1.88%
Dividend yield	0.00%
Volatility factor	47.10%
Expected term (in years)	5 years 3 months 18 days