Leases (Supplemental Cash Flow) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2025	Aug. 31, 2024	Aug. 31, 2023
Leases [Abstract]
Operating Lease, Payments	$ 12,546	$ 12,119	$ 13,153
Right-of-Use Asset Obtained in Exchange for Operating Lease Liability	$ 6,183	$ 3,075	$ 1,654
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Other Assets, Noncurrent	Other Assets, Noncurrent