Employee Benefit Plans - Components of Net Periodic Benefit Cost (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Pension Plans
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Service cost	$ 73	$ 72	$ 71
Interest cost	147	104	104
Expected return on assets	$ (101)	$ (118)	$ (131)
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration]	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent
Amortization of prior service cost	$ 21	$ 21	$ 55
Amortization of net loss		20	36
Other events	(12)	(10)	49
Net periodic benefit cost	128	89	184
SERP
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Service cost	486	919	1,100
Interest cost	1,191	928	943
Amortization of net loss		516	821
Other events		(855)
Net periodic benefit cost	$ 1,677	$ 1,508	$ 2,864