Change a property (eg. view layer) of all Blender windows at once (hotkey or script)?

If I have more than one Blender window open (of one project), how can I change a window property for all the windows at the same time?
Use case: I use predefined hotkeys to change the view layer, as per the tip here: Tip: Key binding for altering properties . --> Using the operator “wm.context_set_value” to set “window.view_layer” equal to “bpy.context.scene.view_layers[“NAME OF VIEW LAYER”]”.
Now, when I have more than one window open for a project, I would like to switch them all at once, not one-by-one. Is there a way to do this with the keymap, or maybe a script?

On a related note, when switching the view layer, the new layer “fades in”, but the old one often doesn’t completely “fade out”, gets stuck. I have to rotate the viewport a bit to get it to update fully. It’s a viewport rendering glitch. Anyone has this? Is there a way to force the 3D viewport to redraw without rotating/panning/zooming/etc. the view?