Condensed Consolidated Statements of Redeemable Preferred Stock, Convertible Preferred Stock and Stockholders' Equity (Deficit) - USD ($) $ in Thousands	Common Stock.	Additional Paid-In Capital	Accumulated Deficit	Redeemable Preferred Stock	Convertible Preferred Stock	Total
Balance at Jan. 03, 2021				$ 16,412	$ 117,038
Balance (in shares) at Jan. 03, 2021				7,500,001	3,129,634
Increase (Decrease) in Temporary Equity [Roll Forward]
Series B\B-1 redeemable preferred stock issuance				$ 2,908
Series B\B-1 redeemable preferred stock issuance (in shares)				1,450,000
Balance at Apr. 04, 2021				$ 19,320	$ 117,038
Balance (in shares) at Apr. 04, 2021				8,950,001	3,129,634
Balance at Jan. 03, 2021	$ 18	$ 10,622	$ (179,641)			$ (169,001)
Balance (in shares) at Jan. 03, 2021	17,462,283
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Equity-based compensation		432				432
Net income (loss) and comprehensive income (loss)			(1,375)			(1,375)
Balance at Apr. 04, 2021	$ 18	11,054	(181,016)			(169,944)
Balance (in shares) at Apr. 04, 2021	17,462,283
Balance at Jan. 03, 2021				$ 16,412	$ 117,038
Balance (in shares) at Jan. 03, 2021				7,500,001	3,129,634
Balance at Jul. 04, 2021				$ 19,320	$ 117,038
Balance (in shares) at Jul. 04, 2021				8,950,001	3,129,634
Balance at Jan. 03, 2021	$ 18	10,622	(179,641)			(169,001)
Balance (in shares) at Jan. 03, 2021	17,462,283
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) and comprehensive income (loss)						6,969
Balance at Jul. 04, 2021	$ 18	11,735	(172,672)			(160,919)
Balance (in shares) at Jul. 04, 2021	17,462,283
Balance at Apr. 04, 2021				$ 19,320	$ 117,038
Balance (in shares) at Apr. 04, 2021				8,950,001	3,129,634
Balance at Jul. 04, 2021				$ 19,320	$ 117,038
Balance (in shares) at Jul. 04, 2021				8,950,001	3,129,634
Balance at Apr. 04, 2021	$ 18	11,054	(181,016)			(169,944)
Balance (in shares) at Apr. 04, 2021	17,462,283
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Equity-based compensation		681				681
Net income (loss) and comprehensive income (loss)			8,344			8,344
Balance at Jul. 04, 2021	$ 18	11,735	(172,672)			(160,919)
Balance (in shares) at Jul. 04, 2021	17,462,283
Balance at Jan. 02, 2022	$ 38	222,080	(177,596)			44,522
Balance (in shares) at Jan. 02, 2022	38,421,124
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Issuance of common stock for vesting of restricted stock units (RSUs)	$ 1	(1)
Issuance of common stock for vesting of restricted stock units (RSUs) (shares)	228,387
Issuance of common stock for special compensation award (shares)	208,914
Shares withheld for withholding tax on RSUs		(265)				(265)
Shares withheld for withholding tax on RSUs (in shares)	(28,295)
Offering costs related to Initial Public Offering		(290)				(290)
Settlement of distributions payable to former Class P unit holders		2,648				2,648
Equity-based compensation		5,126				5,126
Net income (loss) and comprehensive income (loss)			2,043			2,043
Balance at Apr. 03, 2022	$ 39	229,298	(175,553)			53,784
Balance (in shares) at Apr. 03, 2022	38,830,130
Balance at Jan. 02, 2022	$ 38	222,080	(177,596)			44,522
Balance (in shares) at Jan. 02, 2022	38,421,124
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss) and comprehensive income (loss)						8,042
Balance at Jul. 03, 2022	$ 39	231,940	(169,554)			62,425
Balance (in shares) at Jul. 03, 2022	38,931,050
Balance at Apr. 03, 2022	$ 39	229,298	(175,553)			53,784
Balance (in shares) at Apr. 03, 2022	38,830,130
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Issuance of common stock for vesting of restricted stock units (RSUs) (shares)	196,808
Shares withheld for withholding tax on RSUs		(805)				(805)
Shares withheld for withholding tax on RSUs (in shares)	(73,195)
Equity-based compensation		3,447				3,447
Forfeiture of unvested restricted stock (in shares)	(22,693)
Net income (loss) and comprehensive income (loss)			5,999			5,999
Balance at Jul. 03, 2022	$ 39	$ 231,940	$ (169,554)			$ 62,425
Balance (in shares) at Jul. 03, 2022	38,931,050