How high does the house rise - how high to pile up earth (cellar depth low)?

A lot of correct and good tips have already been given. Maybe "demolition and new construction" is still missing. ;) Just as a completely different idea (and without knowing the floor plan, etc.): How about a solution that doesn’t build anything up, but rather accepts the situation at ground level? So thinking of the basement more as a kind of souterrain? The ground floor as a raised ground floor? Maybe the entrance could be moved to the basement? Balcony with stairs in front of the former entrance or terrace door? Plaster everything yellow and do something with the garden at basement level?

According to Labo, you are allowed to fill up 2 m.

Your budget does not allow for filling and retaining. Moreover, as a neighbor I would take legal action. I would murder for the trellis.

Entrance
Relocate stairs or into the "basement."
The stairs should not be too steep but easily walkable.
Bicycles and garbage bins can be neatly stored there.

Small door in front
Balcony connected to the terrace.
Plaster below
Plan parking spaces in that area. With some luck, the balcony can be connected to the carport.
In the area of the double door
fill up 2 m with retaining wall. Sloping towards the neighbor in several plantable/usable steps
backwards to the original level.

After the plasterer comes again, everything in uniform yellow. Finally, no white with Smokey Eyes.

At first, I also thought April 1st. Why a basement on such a property?
An expert won’t help much, the TE always agreed to this nonsense. What was the GU thinking? At least he could have pointed out realistic costs. The property would have been so easy and cheap to develop. No one advised you against the basement. Which is now not even one.

What are the plans for the building authority?

We also did not plan the exterior plastering exactly right in the basement. Now a bit more is exposed than previously planned. It was no problem to just have it plastered later.

The small patio door can quite easily have a fall protection installed.

I also know large balconies and have even seen one around the corner, so it’s possible.

In our neighborhood someone in the south completely piled up a mountain for the terrace and directly next to it on the west side the basement as a living basement is completely exposed. So that works too.

I would also recommend a good garden landscaper, there are solutions. But the outdoor facilities of our neighbors on the steep slope tended to cost six figures. That is now of course somehow outrageous when it was about saving the 1000€ expensive lifting system...

How high is the natural ground actually (that is, how much did you excavate for the construction of the basement)?

How high is the natural terrain actually (in other words, how much did you remove for the construction of the basement)?

I had just been wondering about that myself. I find that in the photo, the trees in the background of the first picture appear to be standing significantly higher. If there’s about a meter difference anyway and you would want to level that out, maybe we’re only talking about a meter above the terrain and not two anymore? In the photo from the side looking at the front door, the neighbor’s flowerbeds are also higher (although not nearly as high as the door). Building some up, handling some with steps sounds not too far off to me. I also have the feeling that "this didn’t have to be the case" and that a level entrance without much fuss would have been possible, but oh well. The child is in the well and all that.

Regarding the terrace, I think there are quite a few options. I’m also running through in my head a bit what I’ve seen with hillside houses before... Something like: terrace as a "deck"/balcony-like and from there you go down into the garden by stairs. Or planning the terrace on several levels. Or first a stair descent to the terrace, which is more at garden level (or slightly above). Or not having the terrace directly on the house and curving a bit of a path there (possibly with a few steps here and there). Or or or... How realistic any of that is in your circumstances, I can’t judge.

One way or another, you’ll probably need a good garden landscaper. Digging through the previous drafts again is certainly not a bad idea either, but breaking away from that a bit is probably better.

And as has already been said: if you don’t include the side door in the terrace planning, you’ll probably need a fall protection there. But I think that’s the smaller problem :)

According to Labo, you are allowed to fill up to 2 m. Your budget does not allow for filling and catching. Besides, as a neighbor I would take legal action. For the trellis I would murder

It wouldn't be more than 2 meters of fill height anyway. We would get the fill material for free from other construction sites. What would be the basis for a neighbor's legal action?