First draft from the draftsman for our single-family house

Do you have this steep slope or a consistent gradient throughout? I don't see a third floor with this budget... If it is actually that steep, then you can also have the house cantilevered so that windows fit on the side, provided that the building window and so on allow it.

Do you have this steep slope or a consistent incline throughout? I don't see a third floor with that budget... If it is really that steep, you can also let the house project forward so that windows fit on the side, provided building envelopes etc. fit.

No, it is not that steep. The incline is quite evenly distributed over the property.

and to distance yourself from the thought "downstairs (residential) basement, on top a normal single-family house"

"Worse" yet, the other way around: a normal single-family house with a residential basement inserted underneath.

Your picture reminds me of this thread: and also in September we had this example with the living room in the basement; or if you want an example of a house with a ridge crossing the slope: in post #18 you can see the house of from the outside.

This is how a basement living area can look. It has nothing to do with dark and damp.

Living spaces belong to the garden for children.

Build your house without a granny flat with as little earthwork as possible. In-laws have a split-level; the house is not noisy.

I am still not clear about your property's slope. At first, it was 3m over the length of the house. That would correspond exactly to one story height. If it is now 3m over the entire property length, that is not even 1m at the house length. I don't see a basement in your budget and a completely different planning.

This definitely needs to be clarified. Try to measure the property vertically. That is the basis for your planning.

Parents-in-law have a split-level house that is not noisy.

Correct, split-level itself does not necessarily mean you have to build it the way it was done forty years ago.

At first it was 3m along the length of the house. That would correspond exactly to one story height. If it is now 3m along the entire length of the property,

... that would be a completely different basis.