Hi everyone,
I am having the same awful experience with this mouse. It not only stutters, it also makes any other device connected via bluetooth virtually unusable (e.g. AirPods disconnecting every few minutes and getting stuck while trying to reconnect).
Also, I made the stupid move of purchasing the "Mac" version without realizing that it's identical in features to the PC version, but it does not have a USB dongle in it, so I'm stuck with bluetooth unless I purchase a dongle separately -.-
After trying many possible solutions I read in this thread and around the magic world of the Internet, I thought I could directly attribute responsibility to something related to the mouse, not the Mac's bluetooth.
Also, my wife uses a Logitech triathlon mouse and it had the exact same problems of my MX master 3, pointer stuttering badly and affected other bluetooth connections, so it's not about the specific mouse.
I think the problem may well be the Logitech Options software.
After reading the post by shahin787 I tried uninstalling it completely but instead of reinstalling it, I tried just using the Mac mini built in drivers and I have not reinstalled it: pointer is smooth now and no BT disconnections. I am also keeping USB 3 devices (a hard drive and a webcam) always connected and I have had zero issues so far, so I don't think this is about interference.
It's a shame because this means I cannot change the mouse settings as I'd like to, but at least I can use it without going crazy every time it gets stuck and affects every other device connecting to the Mac via BT :)