Stock-Based Employee Benefit Plans - Assumptions Used to Estimate Fair Value of Stock Options (Details) - Equity Option [Member]	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average expected term (years)	4 years 5 months 15 days	5 years 2 months 23 days	4 years 5 months 4 days
Expected volatility (range), minimum	33.60%	33.40%	32.90%
Expected volatility (range), maximum	33.90%	35.50%	34.10%
Weighted average volatility	33.70%	33.50%	33.20%
Risk free interest rate, minimum	4.18%	3.40%	1.18%
Risk free interest rate, maximum	4.30%	4.49%	2.85%
Weighted average expected dividend yield	0.00%	0.00%	0.00%