Focus breathing is an optical property of the lens you're using. It has nothing to do with the camera, or with firmware; it's caused by the way the glass elements in the lens move when focussing. Some lenses have it more than others. Cine lenses are often engineered to minimise breathing, but this costs more. It also has nothing to do with light levels, although it will be more noticeable with the aperture wide open, which you would often do in low light.
As for why the R6 seems better -- as far as I know, the R6 mk I does not have focus breathing compensation. (The II does; i.e. it will digitally zoom the image to compensate for breathing. However this is only supported on certain lenses, and there are no EF lenses on the list.)
So I would guess that if you do a like-for-like test on the R6, specifically with the same aperture, you will likely see the same breathing. There's really no way the camera can make a difference. Or, what you're seeing isn't actually focus breathing. Can you describe EXACTLY what you're seeing?
As for the touch screen -- that's a completely separate issue, and it has nothing to do with the lens. It would be better to start a separate topic for that kind of thing. If it's really not responding, then it may be broken and need repair. Can you give specific examples of things it doesn't repond to?
