That’s crazy!! So fun. I had something similar happen with a parakeet years ago. It flew outside and was gone for a couple of days in rain and chilly temps (Florida type chilly). I was a teenager, and was calling for it one morning and it flew to a fence and it jumped on my hand and I took it in. Are you excited about keeping it if you can’t find the owner? Have you called the vets in your area?
Tammy