Share-based Compensation - Schedule of Assumptions Used to Estimate the Fair Value of Each Stock Option on the Date of Grant Using a Black-Scholes Option Pricing Model (Details) - Stock Option - $ / shares	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected term (in years)	4 years 3 months	4 years 2 months 23 days	4 years 2 months 1 day
Risk-free rate of return (in percent)	4.20%	4.40%	4.00%
Expected volatility (in percent)	22.00%	24.10%	28.60%
Expected dividend yield (in percent)	0.80%	0.80%	0.80%
Fair value per option granted (in dollars per share)	$ 73.55	$ 62.55	$ 57.31