When you defeat a villain's first stage, they change to Stage 2 (or 3 if you're on expert.) Do any status tokens fall off, since it's a new object, or does everything transfer over? I'm 50-50 on this. On the one hand, it seems to treat each stage as a separate object, with 'when revealed' effects and being 'defeated' stage by stage, but on the other hand, I'd be surprised if you could get rid of villain upgrades just by pushing them to the next phase.

It's in the rules, everything stays.

Extra damage doesn't carry over, but everything else does.