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

Well, take out the garage, smaller footprint, attic conversion for now without interior finishing, that should save a bit.

And, 2 floors .. do you mean basement and only ground floor? Because there is this slope after all.

And, 2 floors .. you mean then basement and only ground floor? Because this slope is probably there.

Yes. But what I mean is irrelevant. Maybe I also "misread".

At the moment, we are considering completely changing everything by putting the children's rooms and children's bathroom in the basement, redesigning the floor plan on the ground floor, and building no knee wall and a steep gable roof on the top floor for the parents' area.

There is no gable roof so steep that one can get a standing height "within sight" at a reasonable distance from the eaves even without a knee wall. And by the way, it wouldn't be cheaper either. Not to mention the appearance of a spearhead gable side on a hillside house or even on the valley side. A house that practically looks like a captain's gable as the Eiger north face – no thanks.

Apart from that, the children are only in the planning stage. Who knows, in the end we might not be able to have any at all....

I rarely drink wine; with many bottles, it is not even clear in which year they will be opened. Of course, they are stored in the basement with such an uncertain future. But when it comes to drinking, you do bring them upstairs again. In my opinion, that cannot be transferred to having children :-(

With the roof, if it really doesn’t make sense otherwise, you can also consider a small knee wall. In principle, with a 45-50 percent pitch, there should be enough space for a bedroom + dressing room + bathroom?!? A later expansion is not an option. There isn’t that little money available now either. For children’s rooms in the basement, there would be a carport instead of the garage. I can post sketches later showing roughly how I had planned it...

In principle, there should be enough space for a bedroom+dressing room+bathroom at a 45-50 percent slope?!? [...] I can post sketches later on how I roughly planned it...

"Space" and "space with standing height" differ quite a bit without a knee wall. In the drawing scale, laypeople usually won't notice how a roof pitch will visually appear afterwards.

In principle, with a 45-50 percent pitch, there should be enough space for a bedroom + dressing room + bathroom, right?!?

Absolutely. You will probably achieve almost a second full floor in the attic or just barely miss it, as well as additionally having an attic.

I can post sketches later to show roughly what I had in mind...

Yes, go ahead and do that.