I just received the Archaeologist badge on Stack Overflow:
When I clicked Track the next one, I was displayed a choice of the tag badges I had made progress in instead:
Then when I clicked on the "Bronze" tab, I was displayed a tag badge I had already received (the Laravel bronze tag badge):
I closed the modal, and clicked Let us pick. SO picked the Curious badge, and told me that my most recent (non-tag) badge was the Laravel tag badge.
Clicking on the settings cog after this displayed the correct badge modal (i.e., the non-tag badges).
FWIW, my most recent tag in the Badges section of my SO profile is currently the Laravel bronze tag badge, the Archaeologist badge not having shown up there yet.