Global search seems to work now, but I've noticed a strange behaviour, I don't know if it was the same before. If there are too many results, only one page (30 results) is returned. I've tried to search for the word "project" on all forums: if I use an unlimited date range, or 400-1000 days, I get 1 page. If I limit it a little bit more, to 500-1000 days, I get 34 pages of results.
I have no idea if it has something to do with the new host, though. Maybe it is even a strange "feature" of SMF.