Good question. I’ve never done fly-by-wire for aircrafts. But I guess you need to build everything around “Horizont”. So when you move stick to pitch or roll, you are setting desired orientation in relation to Horizont in world space. It kind of like a directional arrow in world space. Then error is calculated in relation to that arrow not in relation to the position of the stick.
Not sure about this but I have impression that this is how WarThunder does mouse controls.
Or do you have something else in mind?