External Dislay Connected even though it is Off?

Some times I use an external monitor to extend the display of my 16" M3 Max MBP, OS X Sonoma.

This all works fine and dandy.

The problem is when the monitor is turned off, it is still connected to my mac as though it extends my display. So if I move my mouse past the edge of my MBP built in display, it will get lost somewhere in the netherworld...what? Sometimes it is easier to disconnect and reconnect the mouse to get it back on the the screen!

Is there no way for the system to detect that a monitor is turned off and therefore not there to be used as extended space: a non existent space in which the mouse should not be able to move?

Thanks for any ideas!