Been using the Mx Master 3 (not S) since 3 years now, and I occasionally switch between intel iMac 4k, MB Air M2, and a windows PC. Contrary to your experience, I've never once faced connection problems across any of my machines. It just performs brilliantly.
The only 2 things I don't like about the mouse:
a) The weight -its just too heavy
b) The forward-backward buttons don't work with Safari (or maybe they do, I never cared about installing the Logi software)
Also, one thing that no one mentions about the magic mouse is the feet that it uses to slide/ glide on surfaces - they tend to attract dirt and become sticky more frequently than any other mouse that I have ever tried, so much so that the mouse becomes annoying to use unless you wipe it with a damp cloth every other day. Never faced this problem with the MX master.