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There are a good number of articles online which explain the boundaries around produce grown and harvested during the Shmita year against halachic parameters, but not what happens if one cooks with it accidentally.
Does it cause the food it was cooked with to become non-kosher? Would you need to Kasher pots, pans, and ovens that cooked unlawfully harvested Shmita-grown produce?
R Yehuda Spitz answers your question regarding vegetables grown in a forbidden way (sefichin) (here, next to last paragraph, see footnote 14 for sources)
many Acharonim understand that Sefichin must be treated like all other real deal Issurim (such as non-kosher; albeit Derabbanan). Therefore, they maintain that if someone cooks Sefichin in their pots, not only will whatever mixture they were cooked with become prohibited, but their pots are rendered non-kosher as well, and would require kashering
Since there are many permutations of the issue (incl. whether the vegetables are actually forbidden, whether the issue is annulled in larger quantities and whether this applies to pots only or also to ovens), consult your rabbi before implementing anything you learn here.
