Leases - Summary of Supplemental Cash Flow Information and Non-Cash Activity Related to Leases (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Cash paid for amounts included in the measurement of lease liabilities:
Operating cash flows for operating leases	$ 25,414	$ 25,351	$ 24,154
Operating cash flows for finance leases	393	403	498
Financing cash flows for finance leases	2,049	1,483	1,332
Lease liabilities arising from obtaining right-of-use assets:
Operating leases	15,279	12,000	8,325
Finance leases	$ 3,596	$ 534	$ 445