Earnings Per Share - Schedule of Antidilutive Securities and Outstanding Equity Awards (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 30, 2024	Apr. 01, 2023	Mar. 30, 2024	Apr. 01, 2023
Earnings Per Share [Abstract]
Net income (loss)	$ (2,221)	$ 1,976	$ (802)	$ 4,094
Weighted average shares outstanding — basic (in shares)	10,762	10,762	10,762	10,762
Effect of dilutive common stock awards (in shares)	0	103	0	130
Weighted average shares outstanding—diluted (in shares)	10,762	10,865	10,762	10,892
Net income (loss) per share—basic (in USD per share)	$ (0.21)	$ 0.18	$ (0.07)	$ 0.38
Net income (loss) per share—diluted (in USD per share)	$ (0.21)	$ 0.18	$ (0.07)	$ 0.38
Antidilutive SARs not included in diluted earnings per share (in shares)	525	376	652	516