Well, ok, on Windows if you keep to certain standard elements of Windows API and only use standard widgets you could get close to transparency.
Why can't you just display a blurry rectangle until the mouse cursor goes to the other screen and then you switch the primary resolution from one screen to the other?
I feel like trying to be extremely clever to handle this particular problem would lead to a solution that handles far more common situations much worse for everybody...
If so, good for you, but there are plenty of people who do so.
Hell, in X11 it even sucks if you use the screens one at a time, eg if you turn plug your laptop into the monitor and turn off the laptop screen, and then later unplug and continue your work on the laptop, the scaling will be off on at least one device.
In that case, the approach taken in macOS is nicer - it just hides the half of the window where the pointer wasn't when the window was dragged. While dragging it does a resample of the bitmap to the screen where that part is shown.
OTOH it is questionable if this is really all that important. Most of the time if a window spans more than one screen it's temporary because you are just moving the window from one screen to another.