Why does photos 'edit in' change image app export behavior?
I use Photo Editor and it seems to be able to crop and resize images that other app sends / "shares" to it.

While I don't know exactly why and I don't do any Android development, I think that it could be those two apps provide functionality for "editing only", where the resulting (edited) photo is returned to the handler, in your case, your gallery app, instead of handling by themselves. This could be a possible reason why those apps can't export photos when the photos aren't opened from within the apps.