160m2 detached house in timber frame construction on the north slope with basement

Okay, I think you are right. It was just an idea. We would like to go to the architect, but I don't like the unpredictable costs. Then it will probably be a 2.15m knee wall with children's rooms upstairs and a garage in the basement after all. A shed roof/flat roof combination with a small parents' area in the attic and the rest as a roof terrace would probably not be cheaper than a gable roof over the entire attic?!?

I'm not sure if the stairs in the attic work.

Take out the corner.
You have 2 wardrobes.
Huge entrance area
I find the separation of the children's rooms by the entrance terrible.

You have QM on each floor that can be removed without losses.

Then it will probably be a 2.15m knee wall again with children's rooms upstairs and a garage in the basement.

Why should that help now?
If you want to save money, you park the car outside on the street or at least initially only on the parking space next to the house.

I see the children in the basement (even though that is north), living on the ground floor, parents in the attic, and everything heavily cramped together. You could also put the children's rooms in the attic, but the older they get, the less they like that.

If you have to save even more, you only have the bedroom on the ground floor, as indicated above, and no finished attic!

We would like to go to the architect, but I don't like the unpredictable costs.

The costs are not unpredictable with an architect (they are stated in the HOAI), but without one. The most unpredictable costs of all are incurred when you individualize a Pinterest floor plan yourself. The hope that at least the 1:1 copied floor would be a calculable size will not be fulfilled.

Then it will probably be a 2.15m knee wall after all

You are falling from one extreme to the other, maintaining the pointlessness: the most inefficient knee wall heights in every respect (costs, benefit, construction) are "zero plus almost nothing" and "everything minus almost nothing". This would certainly be equivalent to a full floor, and a roof slope as a "decorative strip on the eaves sides" is especially odd in appearance. Such a thing is only done in extreme necessity to comply with a ridge height restriction.

The helplessness of your approach is a maximum cry for professional help.

A shed roof/flat roof combination with a small parents’ area in the attic and the rest as a roof terrace would probably not be cheaper than a gable roof over the entire attic?!?

A single-surface shed roof of about 10° pitch, as a truss construction, and covered with corrugated metal, would be the most cost-effective. Whether the development plan (or the integration requirement) allows it in the individual case is another question. Roof terraces are never cheaper, see previous paragraph.

I'm not sure if the staircase in the attic works.

Your suspicion is absolutely correct: without a dormer for the stairs, it would result in pygmy headroom.

You need someone who can build on a slope. Someone who doesn’t build a standard 08/15 prefab house on a basement.

Your budget is not so far off that you can’t build at all. You just have to save costs. In my opinion, the best way to do that is to include the basement area in the living space. You should try to reduce the slab size.

Take your last floor plan of the living level
Pantry - large cupboard in the kitchen, you have a storage room downstairs. Get rid of it
Closet upstairs, get rid of it
Home office in the basement
Reduce the hallway size.
Smaller footprint

Upper floor with a reasonable knee wall
Master bedroom, bathroom, dressing room, one large or two small kids’ rooms

Basement bathroom, second kid’s room, office, entrance with closet, building services, utility room,

Have you contacted other general contractors? Possibly the local brick-by-brick home builder.

What does the development plan specify anyway? Roof pitch, roof type, house height

I could still understand that for teenagers, but a children's room in the basement when the children are only "planned" for now? That's unused space for many years...