Segment Information - Reconciliation of Segment AOI (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Segment Reporting, Reconciling Item for Operating Income (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	$ 104,522	$ 75,398	$ 104,797
Interest expense	31,787	29,929	29,681
Other expense, net	9,081	3,552	2,483
Income before income tax expense	63,654	41,917	72,633
Purchase accounting amortization	5,172	5,038	5,636
Goodwill and intangible asset impairment charge	0	36,180	0
Operating Segments | AMS
Segment Reporting, Reconciling Item for Operating Income (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	85,035	92,234	81,445
Purchase accounting amortization	0	0	0
Thailand plant closure inventory write-down	0	0	0
Cyber Event impact	616	3,878	0
Goodwill and intangible asset impairment charge	0	3,838	0
Restructuring, asset impairment, severance, and other, net	2,138	2,420	3,569
AOI	87,789	102,370	85,014
Operating Segments | EAAA
Segment Reporting, Reconciling Item for Operating Income (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	19,487	(16,836)	23,352
Purchase accounting amortization	5,172	5,038	5,636
Thailand plant closure inventory write-down	0	2,530	0
Cyber Event impact	456	1,215	0
Goodwill and intangible asset impairment charge	0	32,342	0
Restructuring, asset impairment, severance, and other, net	3,493	5,769	8,280
AOI	$ 28,608	$ 30,058	$ 37,268