Floor plan for a house on a slope (ground floor and residential basement) with a maximum of 150m²

Also think that for the relatively small house with 2 children's rooms + dressing room, an open space is too much luxury.

Could you explain in more detail what exactly you mean by the vestibule? I'm not sure if I understand it correctly.

If I remove the airspace and then put a door next to the stairs, it would be an absolute darkroom behind it. Furthermore, you'd have a door there but right next to it, the stairs are open to the back.
Maybe I have completely misunderstood it

More or less you understood it correctly, no matter what the fine tuning on the floor brings now.
It is as it is: a house needs space at the entrance for coats, bags, shoes. I'd say at least 60 cm width per person.
Without a wardrobe or closet, the entire hallway will become cluttered. There is no other place to take space from than the unnecessary airspace.
How do you imagine coming home? Apparently, that you come in and admire the view through the panoramic window.... Jacket and shoes, that doesn't exist
Do you have little helpers at your place who make your stuff disappear?

Just quickly sketched on the phone.

Without paying attention to details or measurements but so you have an idea of what I mean.

Possible planning without airspace: I would relocate the entrance so that not everyone who rings the doorbell is immediately standing in the private area. However, I cannot position the entrance on the garage side without a reason, because otherwise the bathroom would have no window. So you first have to tiptoe past the bedroom window – hmm. Instead of a dressing room, I would plan a walk-in closet with frosted glass doors, since the garage does not allow for a window. Due to the separate entrance, the private upper floor is somewhat shielded.

The cardinal directions are also difficult to incorporate. Unfortunately, the children's room is only in the north. Do you have any other ideas?

Edit: Ah, Not bad either! However, then again a child is next to the garage.

I just realize that I forgot to mention that the dressing room is not a must. This is more based on the suggestion of the general contractor. If a normal sliding door wardrobe fits into the bedroom without any problems, that is fine with us as well. But the last proposal really looks reasonable, even if in this case we would have to say goodbye to the air space. : As already written before, what would actually bother me here is that without the air space with a window behind the door, it is pitch dark. That is why this is rather not an option. Nevertheless, thank you for your efforts.

The cardinal directions are also difficult to incorporate. Unfortunately, the children's room is only in the north. Do you have any other ideas?

Nope.
On the one hand, I’m completely unfamiliar with the plot (one might come up with the idea to place the garage on the left side of the plan), on the other hand, I don’t believe that someone would say goodbye to their beloved airspace with panoramic windows within half an hour just because a forum thinks so.