Income Taxes - Significant Components of Deferred Tax Assets and Liabilities (Details) - USD ($) $ in Thousands	Dec. 30, 2023	Dec. 31, 2022	Jan. 01, 2022
Deferred tax assets:
Estimated contractual adjustments	$ 16,282	$ 13,589
NOL, federal and state	24,952	30,175
Tax credits	2,134	2,688
Payroll related accruals	21,755	18,742
Intangible assets and goodwill	90,945	80,629
Interest expense limitation	80,644	59,871
Transaction costs	3,257	3,608
Accrued expenses	995	3,642
Lease liabilities	15,189	15,589
Stock compensation	10,164	8,481
Section 174 costs	2,706	1,079
Other	18	310
Gross deferred tax assets	269,041	238,403
Less: valuation allowance	(244,865)	(203,370)	$ (105,000)
Net deferred tax assets	24,176	35,033
Deferred tax (liabilities):
Property and equipment	(990)	(1,363)
Interest rate derivatives	(11,120)	(18,456)
Lease right of use assets	(12,998)	(14,254)
Other	(3,927)	(4,804)
Gross deferred tax (liabilities)	(29,035)	(38,877)
Net deferred tax assets (liabilities)	$ (4,859)	$ (3,844)