I just did this on mine. One of the four corner pads came apart when I tried peeling it off, with one side the smooth surface and foam, and the other side the foam and then the sticky part that was attached to the bottom of the mouse.
The mouse body is slightly hinged, with a clip in the back but the front end (where the charger port is) just swings away from the main body.
Inside, the battery replacement was super-straightforward, except that as noted the old battery is glued pretty well to the plastic mouse body. Just use a screwdriver or something as a lever and try to not crack the plastic, slow steady increasing pressure, and it’ll come unglued.
I’m going to just try and superglue the slippery foot I broke back together again.
I suspect that will mean it won’t come off the same way in the future and this is the last time I can replace the battery, but who knows. I’ve found replacement feet online but since this model is discontinued, hard to say if they’ll remain available.
Sorry for the lack of pics from the inside but once you get the feet off, unscrew it, and pry the top cover half off the bottom part (which is where all the important bits are) it’s very easy.