Thanks @Benjamin_Bini, that seems to work. The only downside I noticed is that the action seems to depend on the geometry of the screens. Moving "right" doesn’t work on my system because my two monitors are position one above the other, so I had to use moving "down".
I guess when switching to my work monitors, which are positioned differently, that won’t work anymore.
maybe some other action you have configured somewhere that resizes the window?
Especially the "move window to next monitor" action would never resize anything - that is actually a limitation of the action, which is why it only works on same resolution displays.
I’m using my macbook + an external 27in monitor but I don’t think this is the cause: let’s say I open Textedit and move its window on the next monitor, it resizes the window. But if I move it again and again, it doesn’t resize it anymore. It only resizes the window the first time it’s moved. That means it can move the window correctly!