If I had a staircase into the living room, I would keep it in the American style so that the staircase is a design element, with the lower steps rounded and somewhat wider to also offer something for the eye. But you need space for that. In your case, it doesn't really make sense because otherwise there would be a lack of space in the living area. Since the floor plan still has potential, as others have already pointed out, I would have it planned differently again. Where does the plan actually come from? Did an architect draw it?