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

Instead of going to the garden landscaper, I would try to first get a consultation for builders. This is offered by some consumer centers and chambers of architects. Unless the excavation for the construction of the basement was the idea of the builders in order to reduce the costs for the construction pit.

I can hardly imagine a staircase as wide as the double-wing terrace door visually - it would have to connect directly to the terrace door, right?

First a landing and then the staircase. Google "stairs on the balcony" or something similar.

Or Google "stairs at patio door." Then you will find, right among the first results, a double door with stairs leading to a wooden terrace. Something like that is what I meant. So that you go directly up the stairs onto the terrace, which is then also raised by 1 meter, but as far as I understand it now, approximately at the height of the neighboring properties? Then from a layperson's perspective, filling it should be fine, but with such special things always ask an expert, namely a landscape gardener. But if the house then only sticks out by one meter in the end, I think you have a reasonably good solution (still feasible visually and financially).

Instead of going to the landscape gardener, I would first try to get a client consultation. This is available at some consumer centers and chambers of architects.

During the planning a year ago, the lifting system was mentioned, which was then quickly discarded by the general contractor and us, as we all unanimously preferred the alternative, namely raising the house like the neighboring houses plus the retaining wall.

Client consultation for what? For the fact that one decided on the built solution? The OP wanted it exactly as it was built. And now he realizes that his wish was not so good after all.

Instead of going to the landscape gardener, I would first try to get a consultation for building owners. This is available at some consumer centers and chambers of architects.

What could I achieve with the building owners' consultation?

I would have it checked to what extent the GU advised and built correctly. The clients seem to me too inexperienced and naive to be able to assess offers from a garden and landscape contractor. Otherwise, this will be the next debacle. Correctly manufacturing light wells for a basement is not familiar to every garden and landscape contractor. Especially when money is tight, I would seek independent advice. Garden and landscape contractor invoices tend to explode.