Floor plan design for a single-family house 230-235 m² on two full floors

So the main thing is big and square? Well then.

Yes, there are computer representations that I cannot post because of copyright. However, it should not be a problem to quickly simulate different pitch angles with the computer. We will surely ask for comparative representations with 23°, 30°, and 35°, then it will be decided quickly. We quite like the flatter roof.

Oh, thanks for the inspiration for a post on this topic!

You can forget such computer simulations, because they also simulate things that simply don't work or omit significant details. That means they can display a view that will never be "reproducible" in reality: you can zoom the scale as if you had eyes the size of a pinhead or bigger than a fist, plus they can show perspectives that reality contradicts: they can present the planned building as if you were sitting on the attic of the garage of the house after next and could see through all the houses in between like with X-ray eyes. Such perspectives could only be recreated in reality with a camera drone, and you would have to demolish the surrounding houses first. Most people I know perform such operations exactly zero times per week ;-)

Corners, different facade materials, etc. absolutely help make the house more exciting and interesting. That only leads each time to additional costs and thus to the conflict of goals between "beautiful" and "economical."

However, this certainly also applies to roof truss design from an aesthetic point of view.

I wouldn’t say that, but rather that we are looking for a compromise between the three axes [Platz/Nutzung], costs, and aesthetics. We are not fixed on 12x12, but we don’t find it visually unappealing either.

I am also slowly starting to wonder if the post might be trolling. So many strange priorities and considerations from a CEO? So little number sense? Whatever.

Which type of house with which roof shape and pitch would be ideal for just over 200 m² of living space? A rather elongated building was recommended, which, as mentioned, would also be completely fine. If the roof is missing, what would be appealing then?

The open space will be a real highlight statically, about 6.5x11.2m free spanning probably only works with massive beams, corresponding support or secondary beams, or prestressed concrete in really thick sections. But those are then thousands, just such beams spanning across cost independently of the rest of the ceiling, which also becomes thicker.
5m is not much of a problem with partially prefabricated ceilings, with anything above that you already limit your options regarding execution.

If you are really open and it doesn't depend on just a few days, a site plan would be quite good, then one could take a look at what overall could develop, also the topic of access, garage and outdoor area/terrace I wouldn't consider entirely separate from the actual house ;)
I've noticed with us that there always have to be compromises, especially if it is supposed to be optimized, but here "seemingly optimized" often happened. For example: the hallway is small, but the "saved" square meters were reflected in the room, but still only serve as "transit".

With the space, I find two 90° offset rectangles quite interesting, for example, this also allows covered terrace areas or shading to be dealt with right away and it appears distinctly lighter. Garage or carport can also be integrated at that point. Bungalow would also be a consideration with the available space.