My external display is set as the extended display but I can't move the cursor from the monitor to the main computer display.
With Monterey (12.7.1) I set the Macbook Pro (LG Full HD) as the main display. Default resolution for the display. The MacBook Pro built-in Liquid Retina XDR Dsplay shows: use as Extend display, default resolution for display. Preset is Apple XDR Display. Refresh Rate: is ProMotion.
Universal Control has all three options checked.