Can Bangle.js 2 app disconnect from phone and later reconnect?

Well except the iOS case, there it is slightly more complicated with notifications but I think even there you can have one connection out while iPhone is connected.

Also your 4th point "app reconnects Bangle.js 2 back to the phone" is hard to do because the connection is done in reverse. However maybe if watch notices the phone disconnected it could start some connection the other way to ping the phone to reconnect. But gadgetbridge would need to provide service for accepting that.