Joplin itself is AGPL. Unfortunately, Joplin Server is under “JOPLIN SERVER PERSONAL USE LICENSE”.

While I really like Joplin, I’m thinking of making the switch to something fully open source.

I’m not sure what EXACTLY you’d be looking for from a search feature as I’m mostly a light user myself, but there’s a search option which will search the contents of all your notes. I can’t tell you how robust it is, but it does have exclusion (desiredTerm -excludeTerm) search at least, and there’s standard Find/Replace functionality once you’re in the specific note.