Earlier quoted context omitted.
Mail on iOS stopped working properly months ago, touch on this particular device sometimes does not work. Photos app is ridiculous. Software quality is declining. Even very average user like me can notice it.
The Mail thing was weird. I thought it was maybe an update or even a network issue as I had recently changed my router. I eventually gave up and replaced Mail with another email client.
They still haven't fixed it.
I don't use emails enough on my iPhone to make the effort to try another client, but the unread bubble is still stuck at 2, no matter how much unread emails I actually have. The app randomly shows or hides some emails...