I have the drafts for the house here, but not for the basement. There is no draft for it since we actually told him we were building without a basement. [...] maybe the contract for the basement should simply be outsourced to a basement builder, and then the main contractor continues building from the top edge?
That's exactly what I thought. The basement builder only needs the ground floor so that he knows where the load-bearing walls run above it. See the basement in this sense as a slab with technical and storage rooms.
Originally, I actually wanted to have everything from one source.
The main contractor can subcontract the basement builder and manage construction supervision for both, you just arrange the tender process.
And one more thing. Yesterday my father gave me an idea. The plot is about 0.5 m lower than the street. You could build a normal basement as a "black tank" at the same depth as the current basement. So that it sticks out quite far, and then fill up the plot to match the street level.
In principle not bad, especially since without a basement you probably wouldn't want the house to be below street level anyway - among other things because of the keyword lifting station. How was it thought of previously?