Single-family house with a ground-level granny flat on a slope

Of course, you can also place a wooden house on a basement built into a slope. The possibly missing pressure due to the lighter construction method then must be compensated for elsewhere if necessary (earth pressure beam, more partition walls in the basement, thicker basement ceiling). A structural engineer can determine if that is possible; whether it makes sense should be known by the planner/architect.

What you are describing (and I consider it a good idea) is not really a basement, but basically an underground garage with an attached technical room. Of course, this can be constructed much more "roughly," and thus more cost-effectively. If you search from house point DE for "compact living on a slope," you will find another example. That house is not suitable for you, but the cross-section and the design of the basement are quite illustrative.

The problem with a wooden house on a slope is that you have to protect the wooden wall on the slope side. If the wooden wall is far enough above the ground, that is quite doable. However, I am far from certain whether that is feasible for you – the slope is already steep. If you place an imaginary cross-section in the terrain profile, you will see if the lower edge of the wooden wall on the slope side is far enough above potential groundwater on the slope.

The problem with a wooden house on a slope is that you have to protect the wooden wall on the hillside. If the wooden wall is far enough above the ground, that is quite manageable.

No wood should touch the ground. We have a concrete slab and retaining walls, and the wooden house is built on top of that. The concrete slab had a groove, and parts from the carpenter fit exactly onto it. You can possibly see it here.

Of course, you can also place a wooden house on a hillside basement. The possibly missing pressure due to the lighter construction must then be compensated for elsewhere if necessary (earth pressure beam, more partition walls in the basement, thicker basement ceiling). A structural engineer can do that; whether it makes sense should be known by the planner/architect.

What you are describing (and I think that is a good consideration) is actually not a basement, but basically an underground garage with an attached technical room. Of course, that can be executed much more "roughly," and thus more cost-effectively. If you search from House Punkt DE for "compact living on a slope," you will find another example. The house may not suit you, but the layout and execution of the underground floor are quite illustrative.

The problem with a wooden house on a slope is that you have to protect the wooden wall on the hillside side. If the wooden wall is sufficiently above the ground, that is quite feasible.

Many thanks, that’s pretty much how I tried to explain it—only that instead of stilts at the front, the garage protrudes halfway.

Can I protect the hillside wooden wall with a watertight concrete wall, practically like a formwork? I assume that is cheaper than building a full basement because it should be possible since basements are also made of concrete and have to withstand water.

No wood on the ground.
We have a concrete slab and supporting walls, with the wooden house on top. The slab had a groove that parts of the carpenter fit exactly into.
You can possibly see it here.

As I understand it, the idea is:

Garage with technical room offset under the house
Concrete wall at the height of the garage
A concrete slab covering the entire footprint including garage
House on the concrete slab

Is the thought and feasibility correct?

Here you can possibly see it.

By the way, it looks great

Yes, that is fine. Our concrete construction has 3 floor slab levels on different slope heights, as we have a small basement room centrally under the balcony on level -1 (not under the house), a large floor slab on level 0, and another floor slab raised to level +1 in the left part of the house. The foundation is thus stepped, and the left part of the house is partially built into the slope and not on top of it. Here you can see the three levels indicated before the concrete work began. I don’t have the concrete photos right now. The foundation walls were insulated on both sides and backfilled on the slope side.

You need basement-side WU concrete and no additional wooden wall

With us it is executed as follows
Basement side on the ground floor WU concrete insulated on both sides
Floor slab concrete
Remaining walls solid wood
Upper floor all walls solid wood

Reinforcement in the ground and in the retaining wall was intense. The construction company has never needed that much before.
Ceiling ground floor/upper floor extra thick, also a premiere.
Garage is executed simpler.
Concrete wall and normal floor slab. The garage stands next to the house.

However, wooden studs supported on 4 walls massive in the basement or retaining wall and the house then 1 m in front completely wooden studs