180 sqm non-replacement house, best adaptation to the plot?

Uh, that rules out almost all suggestions

Easy :D, the barn is still ONE option out of three. Although a good one.

I don't understand your concern. Two are allowed, right?! Barns are visually two-story buildings

Aren't quite a few of the houses that I would also classify as barns one-and-a-half stories with a very high knee wall? (=visually two stories). But two full stories plus a steep gable roof could be somewhat tall (and a bit too much living space). The photo I attached was indeed a nice gray-beige two-story (except for the windows?).

At least 3m downstairs. Maybe also a gallery or very open staircase. Barns are airy and tall. No projections or recesses. Actually totally the opposite of the design with slanted walls.

YES, that’s exactly how I see a barn. And yes, the design with the slanted (dining room) walls is basically the counter-design to the barn, with a flat roof (although: there's still "room for something";), a combination) I’m trying to finish it tomorrow... One has to go to sleep now :)

Barn houses from Scandinavia

Yes, Scandinavia can do that... I even know an architect here in Berlin who was/is a master carpenter in his first life... has done great things, but I would only get a wooden house approved in the area with the administrative court :)... and probably not even then.

Aren't quite a few of the houses ones that I would also classify as barns,

I have no idea which quite a few houses you know...

1/2 storeys with a lot of knee wall? (= visually 2-storey). But two full storeys plus a steep gable roof might be a bit tall (and somewhat too much living space). The photo I attached was indeed a nice gray-beige 2-storey (except for the windows?).

...and the discussion about whether a barn is one or two storeys is unnecessary, since a barn has no living storeys.
First, have something nice planned in 7.5 x 13, nicely open to the south. Either way it is worth experiencing :)

You unfortunately withhold the development plan from us, but is there a restriction on the maximum building height or eaves height? 3 m clear room height on the ground floor is already quite a statement that can quickly throw a wrench in the rough calculation.

Such an open gable would have somehow been my wish, but unfortunately it didn't work out. Well, for the next house... :)

is there a restriction on the maximum building height or eaves height?

I am not withholding anything here, the initial development plan from 2017 contains only minimal provisions because it is only about preservation of the existing situation and exclusion of inner-area development. The surrounding buildings reach heights of 9-11m.

Here are all the provisions:
Floor area ratio: 0.25
Plot ratio: deliberately not specified
2 full floors
7.5 m front yard, to be landscaped.
That is all.