Share-Based Compensation - 2019 Stock-Based Incentive Compensation Plan (Details) - USD ($)	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Shareholders' Equity and Share-Based Payments
Common stock, shares authorized (in shares)	75,000,000	75,000,000
Options
Outstanding at the beginning of the period (in shares)	224,374	57,584
Outstanding at the end of the period (in shares)	361,613	224,374	57,584
2019 Plan
Shareholders' Equity and Share-Based Payments
Number of shares of common stock available for awards	750,000
Common stock, shares authorized (in shares)	139,691
2019 Plan | Employee and Non Employee Stock Option
Options
Outstanding at the beginning of the period (in shares)	224,374	57,584
Granted (in shares)	161,613	224,374	0
Exercised (in shares)		(57,584)
Cancelled (in shares)	(24,374)
Outstanding at the end of the period (in shares)	361,613	224,374	57,584
Vested and expected to vest (in shares)	225,000
Weighted Average Exercise Price
Outstanding at the beginning of the period (in dollars per share)	$ 8.19	$ 7.1
Granted (in dollars per share)	7.7	8.19
Exercised (in dollars per share)		7.1
Cancelled (in dollars per share)	8.21
Outstanding at the end of the period (in dollars per share)	7.97	$ 8.19	$ 7.1
Vested and expected to vest (in dollars per share)	$ 8.18
Aggregate Intrinsic Value
Outstanding at the beginning of the period (in dollars)		$ 88,104
Exercised (in dollars)		$ 28,792
Outstanding at the end of the period (in dollars)			$ 88,104