Interesting!  I was not familiar with that system preference nor that it would just (sort of) work in IDLE; I'm presuming that there is nothing in IDLE that knows about this.  I'm not sure whether Tk gets that behavior for free (because of the use of an underlying macOS API) or whether it is intended to be supported behavior.  Or what would need to be done in IDLE to fully support it.  Perhaps Kevin might be able to give some guidance from the Tk perspective.

Ah, I see that if the selected tab is an edit window rather than the IDLE shell window and then one uses the cursor to resize the window (grabbing the bottom right hand corner), the cursor location info reappears and then seems to behave as expected: disappears when selecting the shell tab and reappears when selecting the edit tab.  Further, when opening yet edit window, the cursor info is missing on the new edit tab but still present on the previous edit tab; resizing the window again causes the cursor info to now appear in the newly edit tab.  So all of this seems to be IDLE-specific.