If you can put it all back together you can. I'd just be a little worried that the threads in the BB shell were damaged. And that might be an issue for even a new BB cartridge. But perhaps it wasn't as loose as your description makes me imagine.
Examine your bike closer more often. If you wipe the grime off your bike every other ride or so, then you'll be seeing first hand much of the stuff you should be checking for issues starting to happen.
Was that original to the bike? I've never had a BB loosen up, with the exception of my first attempt at adjusting an old Ashtabula crank many many years ago.
Generally BB's are cheap. So depending on the amount of use you give your bike and how much longer you intend to keep it then you might consider putting in a new BB. However that decision might also be tempered by how much I desire to ride today right now.
Last edited by Iride01; 01-11-22 at 09:14 AM.