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Share-based Compensation - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Aug. 30, 2025	Aug. 31, 2024	Aug. 26, 2023	Oct. 31, 2023
Stock Appreciation Rights (SARs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percentage vested after each anniversary of the grant date	33.00%
Expiration period	10 years
Weighted average fair values of Share-Based Awards granted (in dollars per share)	$ 64.32	$ 55.97	$ 60.38
Stock Appreciation Rights (SARs) \| Cliff Vesting
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Period awards become fully vested or exercisable	3 years
Share-Based Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total compensation cost not yet recognized related to non-vested awards	$ 16.9
Period for recognition	2 years 3 months
Time-Based Restricted Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percentage vested after each anniversary of the grant date	33.00%
Period awards become fully vested or exercisable	3 years
Non-Employee Directors \| Unrestricted Stock
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares granted (in shares)	1,662	1,475	1,575
The 2023 Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance (in shares)				375,000
Shares available for future grants (in shares)	352,741
The 2023 Plan \| Non-Employee Directors \| Stock Appreciation Rights (SARs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares granted (in shares)	4,938	5,004	6,864