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Stock-Based Compensation - Stock Options Activity (Details) - USD ($)
12 Months Ended
May 16, 2023
Jun. 28, 2022
Jun. 30, 2023
Jun. 30, 2022
Share-based payment award, options, outstanding        
Outstanding Options, Beginning     73,194  
Options Granted (in shares) 39,330 73,194    
Options Forfeited (in shares)     (7,647)  
Outstanding Options, Ending     104,877 73,194
Options exercisable     13,109  
Weighted-Average Exercise Price, Beginning     $ 11.16  
Weighted-Average Exercise Price, Granted $ 8.90 $ 11.16    
Weighted-Average Exercise Price, Forfeited     11.16  
Weighted-Average Exercise Price, Ending     10.31 $ 11.16
Weighted-Average Exercise Price, Exercisable     $ 11.16  
Weighted-Average Remaining Contractual Life, Granted (in years) 10 years 10 years    
Weighted-Average Remaining Contractual Life, Forfeited (in years)     10 years  
Weighted-Average Remaining Contractual Life (in years)     9 years 3 months 29 days 10 years
Weighted-Average Remaining Contractual Life, Exercisable (in years)     9 years  
Aggregate Intrinsic Value     $ 19,272