One term that seems maybe suitable is overripe, but this seems to be specific to fruits which when overripe exhibit different changes compared to those of vegetables: overripe fruit destructure and decompose, but the vegetables that I’m looking for an adjective for often become tougher, woody perhaps, more difficult to chew, etc.
So it’s not so much that they’re overripe because these qualities may essentially prevent it from even properly ripening.
I also like overgrown, but that usually describes vegetation that has grown out of control, so overloading the meaning of this word seems problematic due to the overlapping context.
An adjective I usually do see used for this is old, but that doesn’t seem to really capture the concept specifically enough.
Maybe late harvest or past due? These compounds do the job to describe it but seem not straightforward to use in a sentence like adjectives are normally used.