Goodwill and Acquired Intangible Assets - Schedule of Changes in Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
Goodwill [Line Items]
Balance, beginning of period	$ 3,461,891	$ 3,358,511
Foreign currency translation adjustments	25,448	26,262
Balance, end of period	3,493,316	3,461,891
Pure Systems Acquisition
Goodwill [Line Items]
Goodwill, acquired		$ 77,118
Other Acquisitions
Goodwill [Line Items]
Goodwill, acquired	$ 5,977