Single-family house design with a gabled roof at the edge of the construction area

I see it the same way as , not using the south and west at all is not optimal. The south is difficult for you (well, it might be possible, but we don't know the building boundaries on the property yet). However, if I assume minimal shifts of the house, at least a north/west terrace with evening sun could be realized ...

could you show us the neighboring buildings? (image, parcels, whatever)

For me, without knowing the building boundaries, I would probably do it roughly like this ... (possibly also orient the house more lengthwise, similar to the plot). With the objection that there is another large house very close to the west.

would you like to show us the neighboring buildings? (Picture, parcels, whatever)

We quickly created a drawing showing the plot, building boundaries, and neighboring buildings.
The blue is the house, the gray is the carport.

I already expected that you wouldn’t be satisfied with the east orientation.
Do you have any good ideas for more evening light?

I would arrange the all-purpose room in an L shape... that way you catch E, S, and W.

Do you mean the 4m all-purpose room width is too narrow? Or in some places too wide?

That would also mitigate the 4 meter width (too little for the length).
Unusual and also not advantageous for the appearance is the orientation of the house combined with the prescribed ridge direction. I wouldn’t make the house deeper than it is wide, because then the appearance suggests a semi-detached house. Also, a stair location on the ridge side makes more sense to get a favorable access to the attic. It is not very pleasant to enter the house and have a three-meter-long side of the staircase next to you.
You somehow twisted the natural course of the house. However, I’m currently only looking at it on my phone and unfortunately have little time to go into suggestions in more detail.
- Vanity under the slant does not work.
- I would never place a toilet in the middle of a house; someday you’ll have a drainage problem and then throughout the whole house... Toilet at the exterior wall under the slope.
- Shower width is overrated; advantages and comfort come from depth. No window in the shower...

Carports only on the sides or in front of the building, no basement replacement rooms in the front garden (5m wide strip between the building and the access road)

What is meant by that? Is it allowed to place the carport with one side next to the sidewalk?
I would probably play around with that a bit.
If the carport stays where it is, I would position the house crosswise, entrance on the short west side, stairway to the north with panoramic window.
Another terrace in the south and also in the northwest.
Sorry for the brevity, I hope it’s understandable

I would never place a toilet in the middle of a house, eventually you have a drainage failure and then throughout the whole house...

I think that's overrated. What could happen or be different?