Goodwill and Other Intangible Assets - Narrative (Details) $ in Thousands	3 Months Ended	12 Months Ended
	Jan. 01, 2023 USD ($)	Dec. 31, 2023 USD ($)	Jan. 01, 2023 USD ($)	Jan. 02, 2022 USD ($)	Oct. 02, 2023	Oct. 03, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Number of operating segments		2
Number of reportable segments		2
Goodwill and Other Intangible Assets [Line Items]
Goodwill, impairment loss			$ 29,384
Goodwill	$ 102,417	$ 105,448	102,417	$ 147,025
Impairment of intangible assets, indefinite-lived	$ 6,300
Impairment of intangible assets, indefinite-lived	6.3 million
Amortization of acquired intangible assets		5,172	5,038	5,636
Finite-lived intangible asset, expected amortization, 2024		5,000
Finite-lived intangible asset, expected amortization, 2025		3,000
Americas
Goodwill and Other Intangible Assets [Line Items]
WACC (percentage)					11.50%	13.50%
Reporting unit, percentage of fair value in excess of carrying amount					71.00%	71.00%
EMEA
Goodwill and Other Intangible Assets [Line Items]
Goodwill, impairment loss	$ 29,400
Operating Segments | AMS
Goodwill and Other Intangible Assets [Line Items]
Goodwill, impairment loss			0
Goodwill	102,417	105,448	102,417	108,505
Impairment of intangible assets, indefinite-lived	3,600
Amortization of acquired intangible assets		0	0	0
Operating Segments | EAAA
Goodwill and Other Intangible Assets [Line Items]
Goodwill, impairment loss			29,384
Goodwill	0	0	0	38,520
Impairment of intangible assets, indefinite-lived	$ 2,700
Amortization of acquired intangible assets		$ 5,172	$ 5,038	$ 5,636