For what it is worth, I did an estimate on here awhile ago (welcome to search my history) where IIRC you had to eat several kilos of boar and mushrooms every day to approach limits for radiation workers (which has a large safety margin).

I think many people forget that we are really good at detecting radiation. This is mostly due to Cold War era fear and so a lot of research got put into this and we have cheap and sensitive devices. Cheap enough that there are large public networks of radiation monitoring set up by citizens. Not too dissimilar from citizen weather projects.