Having the same issue. I am using a Macbook PRO 16 intel i9 - 2019 - 16GB - 1TB; macOS Monterey 12.2.1; My MacBook keyboard, trackpad, and also my external Logitech MxKeys (keyboard) and Mx Master 3 (mouse) are lagging; I have noticed that when I plug an external Monitor, the lag stops. Please solve it, this is very annoying!