Share-Based Compensation - Fair value assumptions related to the 2019 Plan (Details) - 2019 Plan - Employee and Non Employee Stock Option	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Shareholders' Equity and Share-Based Payments
Expected volatility	52.50%	55.10%
Weighted average risk-free interest rate	4.30%	3.70%
Expected lives (years)	6 years	5 years 3 months 18 days	0 years