Single-family house with gable roof approx. 137 sqm, 1 full floor

Oh, so it's the three parcels of land.

Yes, the information is coming in very slowly again. How deep is the building window now?

I count myself among the "carport on the street" faction. I would put it directly in front of the house so that the entire west side remains free for windows.

Yes, the information is coming in slowly again. How deep is the building window now?

I align myself with the "carport on the street" faction. I would put it directly in front of the house so that the entire west side remains free for windows.

Sorry, I thought it was obvious that the two parcels of land behind also belong to the property – I probably didn’t consider everything.

As already mentioned, there is no development plan, so we have to orient ourselves to the neighboring development. The houses there stand on the parcel at the street. So we probably cannot move the house arbitrarily around the entire property. We also oriented the position of the house to the level of the plot since that is where the slope is lowest. If we set it further back, we would have to dig into the slope...
As mentioned, we just don’t like the look of a carport on the street. However, we will discuss this with the architect again.

and where?

Directly from the street to the property.

Carport as boundary construction to the front, garden house to the back. This can be decoupled so that you are open for windows in the west area. I might possibly flip the house, so mirror it. And YES: it means no connection of the 2nd corridor (technical room?) to the carport. That is disadvantageous.

If we now put the carport to the front towards the street, we would have to excavate quite a bit here and probably build with a strip foundation – it’s also a cost question. My wife would like the door to the utility room. I have already said that we should better leave it out in favor of the space – she is not very convinced yet. We'll give it some more thought.

And where is the basement replacement?

Sorry, it’s called "Abstellraum" on the floor plan.

We probably cannot move the house arbitrarily back and forth across the entire property.

That's true: you have a line in the front there that you must adhere to.

I count myself among the "carport at the street" faction. I would put it directly in front of the house so that the entire west side remains free for windows.

I would leave the carport to the side, but in front on the south, so southwest of the house, make a nice large south-facing window. From the open-plan living area. Utility rooms in the east. But you have to see how that fits.

My wife would like to have the door to the utility room. I already said that we should better leave it out for the sake of space – she is not very convinced yet. We'll think it over again.

Then she should participate in such discussions and not just be persuaded by the husband.

Sorry, it means "storage room" in the floor plan.

That is outside. Basement replacement would be inside. That does not exist here. Technology takes up quite some space. Laundry too.
I'll put it this way: with this door in a 7-something sqm technical room, where laundry will also be done, there is no point in further discussion here. That is insufficient overall. Without a door it will be an upgrade to insufficient, one square meter more in the technical room will make it sufficient.
You make it easy for yourselves: you call that a second hallway, and everything will be fine (monkey covering its eyes).

I would leave the carport on the side, but at the front in the south, so SW of the house, make a nice large south-facing window. From the living area. Utility rooms in the east. But you have to see how that fits.

Do you mean something like that? If you give up symmetry, it could work. The living area could get nice west-facing windows.
Maybe the kitchen area in the south then – the light shines through the living area in an open floor plan.
I would then think about a landing/spiral staircase in the east, but then we would also need a new upper floor.