Organization and Summary of Significant Accounting Policies - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Jul. 03, 2022	Jun. 27, 2021
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	$ (213,433)	$ (175,441)
Other comprehensive loss before reclassifications	1,888	(6,384)
Other comprehensive loss before reclassifications, Income Tax	563	(348)
Net other comprehensive loss before Reclassifications	2,451	(6,732)
Reclassifications:
Prior service credits		8
Actuarial losses	(422)	(369)
Total reclassifications before tax	(422)	(361)
Retirement and Postretirement Plans Reclassifications, Income Tax	99	84
Net reclassifications	(323)	(277)
Other Comprehensive (Income) Loss	2,128	(7,009)
Ending balance	(220,413)	(213,433)
Foreign Currency Translation Adjustments
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	14,685	20,136
Other comprehensive loss before reclassifications	1,700	(6,924)
Other comprehensive loss before reclassifications, Income Tax	606	(220)
Net other comprehensive loss before Reclassifications	2,306	(7,144)
Reclassifications:
Other Comprehensive (Income) Loss	2,306	(7,144)
Other comprehensive loss (income) attributable to non-controlling interest	268	(1,693)
Ending balance	16,723	14,685
Retirement and Postretirement Benefit Plans
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	2,112	1,977
Other comprehensive loss before reclassifications	188	540
Other comprehensive loss before reclassifications, Income Tax	(43)	(128)
Net other comprehensive loss before Reclassifications	145	412
Reclassifications:
Prior service credits		8
Actuarial losses	(422)	(369)
Total reclassifications before tax	(422)	(361)
Retirement and Postretirement Plans Reclassifications, Income Tax	99	84
Net reclassifications	(323)	(277)
Other Comprehensive (Income) Loss	(178)	135
Ending balance	1,934	2,112
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	16,797	22,113
Reclassifications:
Ending balance	18,657	16,797
AOCI Including Portion Attributable to Noncontrolling Interest
Reclassifications:
Other Comprehensive (Income) Loss	2,128	(7,009)
AOCI Attributable to Noncontrolling Interest
Reclassifications:
Other comprehensive loss (income) attributable to non-controlling interest	$ 268	$ (1,693)