Stock-Based Compensation - Schedule of Assumptions for Stock Options Granted (Details) - Performance-based restricted stock - $ / shares	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected volatility, minimum (percentage)	41.50%	41.00%	26.10%
Expected volatility, maximum (percentage)	86.90%	89.00%	67.00%
Risk-free interest rate	4.26%	0.81%	0.23%
Dividend yield	0.00%	0.00%	0.00%
Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grant-date stock price (in dollars per share)	$ 10.31	$ 21.40	$ 14.07
Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Grant-date stock price (in dollars per share)	$ 93.50	$ 142.99	$ 4,318.03