Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	May 31, 2025	Aug. 31, 2024
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 438,309	$ 435,754
Accumulated Amortization	331,027	315,755
Net Carrying Amount	107,282	119,999
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	315,962	314,446
Accumulated Amortization	239,584	228,456
Net Carrying Amount	76,378	85,990
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	82,455	81,482
Accumulated Amortization	53,688	51,023
Net Carrying Amount	28,767	30,459
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,892	39,826
Accumulated Amortization	37,755	36,276
Net Carrying Amount	$ 2,137	$ 3,550