Equity-Based Compensation - Summary of Company's Restricted Stock Award Activity (Details)	6 Months Ended
	Mar. 31, 2025 $ / shares shares
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Weighted Average Exercise Price, Outstanding at September 30, 2024	$ 19.37
Forfeited, weighted average exercise price	22.08
Weighted Average Exercise Price, Outstanding at March 31, 2025	$ 19.23
Restricted Stock Awards
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Beginning balance, Outstanding | shares	107,000
Forfeited | shares	3,000
Ending balance, Outstanding | shares	104,000
Weighted Average Exercise Price, Outstanding at September 30, 2024	$ 14.66
Forfeited, weighted average exercise price	14.66
Weighted Average Exercise Price, Outstanding at March 31, 2025	$ 14.66