Share-Based Compensation - 2019 Stock-Based Incentive Compensation Plan (Details) - USD ($)	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022
Shareholders' Equity and Share-Based Payments
Common stock, shares authorized	75,000,000	75,000,000
Options
Outstanding at the beginning of the period (in shares)	57,584	100,000
Outstanding at the end of the period (in shares)	224,000	57,584
2019 Plan
Shareholders' Equity and Share-Based Payments
Number of shares of common stock reserved for awards	750,000
Common stock, shares authorized	139,691
Number of shares of common stock available for awards under the plan	262,000
2019 Plan | Employee and Non Employee Stock Option
Options
Outstanding at the beginning of the period (in shares)	57,584	100,000
Granted (in shares)	224,374
Exercised (in shares)	(57,584)	(42,416)
Outstanding at the end of the period (in shares)	224,374	57,584
Vested and expected to vest (in shares)	69,796
Options exercisable at the end of the period (in shares)	154,578
Weighted Average Exercise Price
Outstanding at the beginning of the period (in dollars per share)	$ 7.10	$ 7.10
Granted (in dollars per share)	8.19
Exercised (in dollars per share)	7.10	8.26
Outstanding at the end of the period (in dollars per share)	8.19	$ 7.10
Vested and expected to vest (in dollars per share)	8.20
Options exercisable at the end of the period (in dollars per share)	$ 8.19
Aggregate Intrinsic Value
Outstanding at the beginning of the period (in dollars)	$ 88,104
Exercised (in dollars)	$ 28,792	$ 64,896
Outstanding at the end of the period (in dollars)		$ 88,104