MS5320W combo: mouse problem

When I use my mouse in the wifi mode I see that the device works in one window only.  The task bar is inactive and the same is true on the desktop or any other application. The touchpad of my mouse seems to behave in the same way, even after turning off my mouse and unplugging the USB adapter (sign out/sign in is necessary to make the touchpad work again correctly). I have verified that the problem persist not only on my Dell XPS13 (with Windows 10) but also on a Lenovo X1 Carbon (with Windows 11).

I tried to update Dell Peripheral Manager but that did not solve the problem. 

Do you have any suggestions?