Semi-detached house - Which one is the best? Who has experience with that?

Can anyone say something about the impact sound problem?

From a building acoustics perspective, it certainly won't be great, but if you want/can live with it. A continuous load-bearing layer without decoupling by edge insulation strips will at least not meet the state of the art regarding sound transmission on the ground floor. If you also want to work without screed on the upper floor and place the floor covering directly on the concrete slab, it will get really unpleasant with children's rooms upstairs and living rooms downstairs.

A foundation without screed (and without underfloor heating) with Foamglass seems reasonable to me.

Then you can expect a nice game of "Black Peter." According to DIN 18356, concrete structures are not a compliant installation substrate. Your floor installer will surely inform you of this as well. And then, if defects occur—which can definitely happen with non-diffusion-open floor coverings on concrete—you'll be in a very bad position. It can be done. But despite meticulous planning and precise execution, it doesn't have to be good (especially in terms of building acoustics).

The sound problem could perhaps be solved by installing a separation there, apparently the [Haustrennwand] has to be built as a double-layer fire protection wall anyway... please correct me if I am wrong...

And whether the concrete or the screed has a certain residual moisture... what difference does that make for the flooring?

Best regards

The screed is checked to see if it is dry enough

Isn't it the same with concrete?

No idea
I do not want to remove anything from the base plate

Isn't that possible with concrete as well?

The usual methods probably don't work there. We might also build with such a slab, and the supplier provides instructions for floor coverings. There is a specific heating program and a funny method with a plastic foil glued onto the slab.