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.

I have found that every time the problem happens. This is the error that appears in the console, hope this helps

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.