I'm trying to switch the arrangement of displays (I work part of the day on one display, the rest using the other display). This was working under previous OS releases, but Monterey made some changes to this pref pane.
The problem seems to be that KM is holding just a moment too long before starting the drag operation and a contextual menu is opening before the drag operation starts.
In the gif below you can see it happening. It clicks at the center of the right display, then holds to drag it over to the left. But just before the mouse moves for the drag, the contextual menu pops up.