Bought house with unpermitted addition

I bought a house recently and discovered that an addition was built without any permits. I don’t think it is structurally unsound, but I’ve consulted with and architect and a few builders and they all seem to think getting the addition permitted retroactively would be a nightmare, if not outright impossible.

I plan to complete renovations that will require permits (i.e., replacing an old balcony and interior remodels that involve moving walls), but none involve the addition. Will the unpermitted addition come up when applying for permits/during inspections?

INFO: The addition was likely built around 1990.

Also, the unpermitted work wasn’t mentioned in the disclosures (where is should be), but I bought from an estate and legal recourse would require the seller knowingly making a misrepresentation. So I have no recourse there.