If you don't remember more details I am afraid that I cannot help you more. If you want put a photo from Mi Fit to see if any device is connected. Also a reason to not be able to connect Mi Band 3 with a phone is that is already connected with a device.
The last thing you can try is to not charge it until the battery goes to 0% and close and then try again to connect it. It's really strange though. I suppose not even gadgetbridge or Notify & Fitness can see Mi Band.
Fortunately I had the Mac address written I tryed with notify seemed something promising but at the end the mi band rejects connection crap, bad thing is I have charged it 2 hours ago anyway I will wait a month I guess to finish the battery and then retry so dissapointed, thank you so much
Have you tried also to clean the cache of mi fit? From mine point of view it seems that somehow and somewhere Mi Band 3 is connected to somewhere that's why cannot connect to anywhere else. (It's just a guess)!