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

The example only helps to a limited extent here, because not all requirements are covered in these two floors. Would the OP also want/accept an attic?

No idea, but he also wanted suggestions/ideas that might be somewhat different.

Personally, I also quite like the second Schwörerhaus, but in our household, I am the more open-minded one; my better half has found a strong preference for the two full stories. We discussed the details today, and we both like the proportions of the rectangular city villa. Yesterday and today, as suggested, I experimented with elongated floor plans; today we discussed the situation within the building plot.

Despite the understandable weakness in the middle of the building, the rectangle is the best combination of aesthetics and placement on the building plot for us (even if one might wonder how this can be with the size of the plot, this is indeed a point worth considering in the overall context).

Today I tried to incorporate the feedback into a new draft. I will also look for a variant with natural light in the upper floor, but this is not a particular priority for us (we are aware that we might not be part of the majority there). Regarding the statics, I found out that spans of up to just over 7 meters can be covered with standard ceilings.

Despite the understandable weakness in the middle of the building, the rectangle is the best combination of aesthetics and placement in the building window for us

Both floor plans are rectangular. You mean your targeted square. ;) Only shapes with more corners up to a circle offer a less favorable ratio of facade area to living space. Since you generally need a lot of facade area and thus wall space to install windows and place furniture, a square is not ideal and regularly leads to the cluster problem of poorly usable space in the center of rooms.

Today I tried to incorporate the feedback into a new draft.

Your commitment honors you, but since time is somewhat pressing for you: When do you want to put this into professional hands? Not every sketch is a design; otherwise, it would hardly take several semesters at universities to learn design.

Regarding the static calculations, I was able to find out that spans of up to just over 7 meters can probably be covered with the standard ceilings.

Whatever "standard ceilings" are supposed to be. Many parameters can be varied, such as concrete mix, quantity, condition and laying method of the reinforcement steel, beams/girders, total thickness, etc.

That's true, by rectangle of course square was meant. We are currently arranging an appointment; I don't want to forcibly build a house I designed myself, but rather prepare for an architect meeting with an idea. :)

How exactly the ceiling is planned, I unfortunately cannot say. 18 cm thickness can be read in the draft, the ceiling was described as "standard" upon my inquiry, which does not lead to additional costs.

but to prepare myself for an architectural discussion with an idea.

Preparing is good, but I would strongly advise against presenting your "design" to the architect/planner and mentioning that this is how you could imagine it. State your requirements and wishes, and then let them do their work. You might be surprised at what they come up with as a proposal.

From my point of view, this "doodling" mainly serves to identify points that you don't like or to learn which areas need attention to ensure that the requirements are truly met. Nevertheless, the architect should work freely. For example, we spoke with three different architects and received three completely different designs, none of which was exactly what we had imagined, but all of which were absolutely suitable.

The problem with the "Klumpenproblem" (I don't even know the word :D) is additionally that hardly any daylight reaches the middle of the house, so you always have to rely on a light switch. The rooms themselves are dark near the door area because the daylight doesn't reach that far into the room. For you, it doesn't seem to be such a problem, but in everyday life, the constant turning on and off can be really annoying. We even have motion detectors in the utility room, and I want that in the cloakroom as well. It's just awful to have to operate the light switch with things in your arms (laundry, bag, etc). There are plenty of reasons not to build square once you reach a certain size - your experiments combine the reasons ;)