Business Segment Information - Reconciliations of Segment Gross Profit (Loss) to Consolidated Loss Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)	$ 4,764	$ 9,653	$ 5,825	$ 8,216
Selling, general and administrative expenses	11,372	12,063	35,389	35,584
Provision (benefit) for bad debts	179	(56)	1,259	(38)
Restructuring costs			5,101
Other operating expense (income), net	139	324	674	(139)
Operating loss	(6,926)	(2,678)	(36,598)	(27,191)
Interest income	(432)	(554)	(1,710)	(1,615)
Interest expense	2,407	2,073	7,505	5,209
Equity in loss (earnings) of unconsolidated affiliates	604	(158)	311	(539)
(Loss) income before income taxes	(9,505)	(4,039)	(42,704)	(30,246)
Americas [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)	(3,514)	3,158	(17,632)	(14,795)
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)	3,837	2,382	9,143	10,499
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit (loss)	$ 4,441	$ 4,113	$ 14,314	$ 12,512