Stock-Based Compensation Plans - Expense Components (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 17,085	$ 15,347	$ 6,475
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	7,540	5,737	4,287
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	7,412	7,920	796
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	1,000	1,019	990
Other
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 1,133	$ 671	$ 402