Glass door for thermal insulation? What alternatives are there?

I need a good idea. We have bought a really beautiful house that has a relatively open living area. The living room, the entrance hall, and the staircase are not separated from each other (see picture):


We would like to thermally separate the staircase because we do not yet fully heat the upper floor, since 2 rooms are unused. The problem is that the area in front of the stairs is relatively small (a bit larger than shown in the drawing, but there are about 60 cm between the passage door to the hallway on the left and the first steps). We initially considered installing a door there, but then the space behind it would be tight, and we also don’t want two doors next to each other. Additionally, it would take away some light from us.

In our view, an ideal solution would be a glass door with double wings. The question is, however, whether this would really help to reduce heating costs (we have 2 floors + basement) or if we should just save ourselves the effort.

Would there be alternatives?

Better to heat all the rooms - it is cheaper, does not damage the building fabric, and saves you from a construction that does not bring much in terms of thermal efficiency.

Of course, the rooms are not unheated, but upstairs there is currently only a bedroom and hobby room, and we sleep at about 20-21C. If all the heat goes upstairs, we lack it downstairs, and actually we don't need it upstairs.

I fear that a door in front of the stairs is rather unpleasant, especially when going down from above. In my opinion, you would have to save a lot of money to accept the narrowing that would result.

How is the stairwell designed, does it have a warm look that fits well into the rest of the room?

What else comes to mind is maybe a sliding door? One side of the stairs is probably "unusable"? Then the sliding door could open in that direction. As a small gimmick, the (glass) sliding door could be opened electrically by a sensor when entering the stairs from above so that you can glide undisturbed into the open lower living area. From bottom to top, an electric switch would probably be okay, but nowhere near as cool.

How much that can bring in terms of energy efficiency, I don't like to judge, but balcony doors, as far as I know, seal quite well.

Just a first idea from me

The sliding door will probably not fit in terms of space. I have attached a picture. To the left of the staircase is a wall with a door to the vestibule.