BTN2 not working on Bangle1, how to update firmware without button 2?

is there a way to diagnose if BTN2 is physically working and getting the signal to the software, maybe via the development web console?

Yes, absolutely - just go to https://www.espruino.com/ide/ and connect, then type:

BTN2.read() - that'll return the state of the middle button. So you can call it once, then hold the button down and press again, and it should return false first, then true when held down.

Once logged in you could also try E.reboot() which will initiate a hard reboot. I've never seen this being a problem but if button 2's pin state got messed up I guess it could stop it working, and then if you can't force a reboot with the buttons it'd be hard to recover.

I know there were some issues a few weeks back when if you'd updated then it could have stopped the middle button working with some clock faces, so it may be that's the issue you're seeing? BTN2 not waking the clock is something that can be configured in settings too.