Detached house on a hillside, approx. 220 m², 2.5 floors, gable roof - ideas?

We are definitely still considering other ideas to at least spruce up the house a bit. In any case, we are also not in favor of chasing every trend. Nevertheless, we are also thinking in the direction of a [Pultdach] and possibly a [Splitlevel-Haus]. Are there any experiences and opinions on this? Then the house would at least no longer appear so "blocky" and would sit better on the slope.

So I can offer an opinion on split-level: a life on stairs – who wants that anyway?

but the TE's wife wanted to look from the kitchen onto the street.

In the hope that their own children might play obediently within the field of view of the kitchen window, or not to miss when Mrs. Suhrbier passes by?

Nevertheless, we are also considering a shed roof and possibly a split-level house.

Oh, someone must have had a happy childhood in the 80s.

Split level "recommends itself" for plots that have a half-story height difference within the building envelope – here it looks like a whole story in the first picture.

A genuine shed roof can be appealing on a slope – whereas a broken gable roof (= shed roof halves facing each other) is pure 80s (and little else). That inevitably calls for a Kim Wilde poster in the window.

... so as not to miss it when Mrs. Suhrbier walks by?

Presumably. But she is not alone in that desire (and I am not referring to myself).

A view of the street is certainly not the only criterion, but I also do not necessarily want to go 20 steps down when I enter the front door. Is it so unusual not to want your living space, or kitchen, in the basement? The basement = living space argument is clear, but for us it is simply a "no-go," although apparently we are in the minority there....

A view of the street is certainly not the only criterion, but I also don't really want to go down 20 steps when I enter the front door. Is it so unusual to not want to have your living space or kitchen in the basement? The argument that basement = living space is clear, but for us it's simply a "no-go," though apparently we belong to the minority there....

No, I would say neither unusual nor a minority.