Well just to update you all, I have updated to MacOS Monterey 13.4 and the problem with the Bluetooth disconnection with my mouse MX Master 2S and my Keyboard K780 persists.
Topo2099
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I have found that every time the problem happens. This is the error that appears in the console, hope this helps
Same problem here, my Logitech MX Master 2S and my Logitech Keyboard K780 keep randomly disconnecting for a second (Mouse more frequently than keyboard) from my Intel MacBook Air 2020. I even tried re-installing MacOS Monterey from scratch (formatting SSD) but the problem started again from the first boot. At first I thought it was the mouse so I tried my wife's Logitech MX Anywhere 3 and encountered the same problem. I tried the MX Master 2S in a company provided laptop MBP 14" M1 Pro 2021 and until now I have not encountered any problems, yet.
I have already tried the steps described here: https://www.howtoisolve.com/bluetooth-not-working-mac-macos-reset-fixed/
to no avail
Please Apple fix this problem, it is extremely annoying.