I have the “ring Video Doorbell”. These notes may not apply to your model.
You’re gonna hate this, but the instructions for removing the mounting bracket are _ inside the bracket _. You have to remove it first to find out how to remove it.
Anyway, the doorbell hooks onto the bracket at the top, then pivots down. There are a couple of catches and a strong magnet that holds it all into place. Plus the security screws; make sure you remove those first.
I was able to get the bracket off by slipping a knife blade in between the bracket and the unit at the bottom of the unit. Sliding the bracket off would never have worked and I would have broken something if I’d forced it.
But be real sure. If you have a model that slides off, you’ll break it if you do it my way. I can only say that the “ring Video Doorbell” opens this way.