Leases - Additional Information (Details) - USD ($) $ in Millions	9 Months Ended
	May 26, 2023	May 27, 2022	Aug. 26, 2022
Lessee Lease Description [Line Items]
Operating lease payments	$ 6.7	$ 7.3
Right-of-use assets obtained in exchange for operating lease liabilities	$ 10.6	$ 10.6
Weighted-average remaining lease term for operating leases	10 years 2 months 12 days		10 years 10 months 24 days
Weighted-average discount rate for operating leases	6.20%		6.10%
Minimum
Lessee Lease Description [Line Items]
Operating lease term	2 years
Maximum
Lessee Lease Description [Line Items]
Operating lease term	5 years