First draft: 2-storey with staggered shed roof

Can be done that way, won't be cheap. I don't see any major disasters; the bathroom drainage is not shown on the ground floor (in the corner behind the front door). I would change the door swing in the children's bathroom, and I wouldn't put the wall of the S-Class directly in front of the license plate. The "garage canopy" and the passage door are, in my opinion, something unnecessary and redundant. I assume there is no basement (?)

I assume it is without a basement (?)

exactly. That’s why I am still considering a larger garage (the partition wall will then be shifted 20 cm upward on the plan) and a sufficiently sized technical room. The door swing in the children's bathroom is a good hint. Additionally, I would then possibly rotate the entrance to the shower 90 degrees counterclockwise.

After opening the door, you immediately "bump" into the bathtub in the upstairs bathroom; I believe the bathroom still needs planning and also possibilities.
In the basement, I would also close the passage between the garage and the utility room; I would also give the guest toilet on this floor at least a small shower.
The building services room seems rather large for a purely technical room and too close to the living area. Due to its location and size/proximity to the kitchen, I would rather swap it with the utility room and possibly make the technical room accessible only from the outside (garage).
The dressing room could become somewhat dark, and also an endlessly long wall of cupboards? Here I would make sure it is furnished with care because it is quite central and you constantly walk past it.

Would additionally then possibly rotate the entrance to the shower another 90 degrees counterclockwise.

No problem with a curtain.

Do you still see major issues in this floor plan,

Yes, your capital. Anyone can design on a large scale, try paying for it!