Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2025	Sep. 30, 2025
Finite-Lived Intangible Assets [Line Items]
Goodwill (not amortized)	$ 3,412,586	$ 3,493,316
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,698,580	1,853,441
Intangible assets with finite lives (amortized), Accumulated Amortization	894,377	1,028,778
Intangible assets with finite lives (amortized), Net Book Value	804,203	824,663
Intangible Assets, Net (Including Goodwill)	4,216,789	4,317,979
Purchased Software
Finite-Lived Intangible Assets [Line Items]
Intangible assets with finite lives (amortized), Gross Carrying Amount	547,186	639,104
Intangible assets with finite lives (amortized), Accumulated Amortization	388,320	472,357
Intangible assets with finite lives (amortized), Net Book Value	158,866	166,747
Capitalized Software
Finite-Lived Intangible Assets [Line Items]
Intangible assets with finite lives (amortized), Gross Carrying Amount	22,877	22,877
Intangible assets with finite lives (amortized), Accumulated Amortization	22,877	22,877
Intangible assets with finite lives (amortized), Net Book Value	0	0
Customer Lists and Relationships
Finite-Lived Intangible Assets [Line Items]
Intangible assets with finite lives (amortized), Gross Carrying Amount	1,093,024	1,149,262
Intangible assets with finite lives (amortized), Accumulated Amortization	460,800	505,202
Intangible assets with finite lives (amortized), Net Book Value	632,224	644,060
Trademarks and Trade Names
Finite-Lived Intangible Assets [Line Items]
Intangible assets with finite lives (amortized), Gross Carrying Amount	31,982	38,179
Intangible assets with finite lives (amortized), Accumulated Amortization	18,869	24,323
Intangible assets with finite lives (amortized), Net Book Value	13,113	13,856
Other
Finite-Lived Intangible Assets [Line Items]
Intangible assets with finite lives (amortized), Gross Carrying Amount	3,511	4,019
Intangible assets with finite lives (amortized), Accumulated Amortization	3,511	4,019
Intangible assets with finite lives (amortized), Net Book Value	$ 0	$ 0