Floor planning with a narrowing plot

I don't find any of this nice. Primarily, the garage is far too dominant on the property and causes there to be hardly any garden. The hallway is too convoluted, the stairs go 100% through the mudroom... I don't understand this detour at all and it only has disadvantages. The kitchen has no access to the terrace and at the back of the property (in the north) there are unused property niches for that. Overall, it all seems somewhat awkwardly strung together, creating corners and empty spaces just to access a room. The hallway is also completely oversized. And you didn't want empty spaces, did you? To be somewhat more constructive, I lack the inclination to count the boxes in order to roughly get some measurements.

I have now labeled the rooms and added some measurements, I hope this is helpful. The staircase should turn 90 degrees coming from below and go straight up to the next floor.
The spacious garage was at the top of the priority list because we are planning a small workshop area there. Tinkering with cars is my hobby. The garden area is deliberately not too large in order not to have too much work with it. However, I do not consider around 120 sqm of garden very small either.
Yes, I am very dissatisfied with the hallway area, too much unnecessary space. It probably makes sense to shorten the garage and move the entrance further up.
The terrace does not have to be within the building envelope according to the development plan.
The arrow indicates north.
I have also added 2 renderings to make it more illustrative. However, the entrance and the dimensions are slightly different.

Where is the point of the staircase where you start going up from the ground floor?

Furnish your ground floor... wardrobe etc.

Arrow North... do you mean the big arrow in this illustration?

The dimensions of the property would be interesting.

[*]no gallery or "dead" corners

[*]Please no flat roof overhangs

[*]No flat roof => gable roof

Therefore, I wonder what you want to do with the rear "extension".
To get rid of your dead corners, try connecting the house to the parallelism of the garage and not see the building boundary as a building line. The piece that then remains in the area between the house and garage at the top of the property can be used as a workshop. Then place the entrance from the east, that is the driveway. Staircase in the middle of the house to the north as a 2-flight winding staircase. However, I lack dimensions to understand this.

Without wanting to be a party pooper: is there 1. a project budget? 2. a cost estimate for the current design?

Besides the above-average house size, the requirements list Photovoltaics+Storage/KNX/etc. is also not insignificant. This doesn't quite feel right for the presumed budget plot (small, awkwardly shaped, and not exactly optimally oriented). It would be a shame to refine a design here that could end up being significantly over budget.

Regarding the design itself: if the garage plays a central role, I would push the garage more towards the south, possibly partially integrate it into the house, and use the huge flat roof area as a terrace to provide an alternative outdoor space alongside the mini garden (120 sqm is really small). Partially shift the house behind the garage and thereby enlarge the western tip of the garden. However, it would probably then be more of a flat-roof design.

Build the garage higher so that a lift fits in or plan a pit. Creepers are uncomfortable and don't fit under every car. Seriously, the previous commenters have pointed out several things I would consider. Don't subordinate everything to the hobby.