Reportable Segments and Geographic Information - Schedule of Reconciles Total Segment Attributable Earnings Before Taxes and Amortization to Income From Continuing Operations Before Taxes (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2023
Segment Reporting [Abstract]
Total segment attributable earnings before taxes and amortization	$ 1,181,300	$ 1,046,400	$ 642,400
Corporate general and administrative expenses	(148,900)	(145,100)	(141,000)
Restructuring and acquisition costs	(59,355)	(98,918)	(188,404)
Other income	(2,500)	2,100	(5,300)
Interest income	62,894	58,560	40,251
Interest expense	(184,304)	(185,420)	(159,342)
Amortization expense	(2,200)	(18,800)	(18,600)
Income attributable to noncontrolling interests from continuing operations	68,700	59,300	43,300
Income from continuing operations before taxes	$ 915,569	$ 718,152	$ 213,400