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.