From when must the shell construction be dry or sealed?

Correct, only an external plaster will be applied. Between the garage wall and the house wall, both made of cavity concrete, there is about 12.5 cm of insulation. To me, it looks like Styrofoam.

The garage roof is currently being sealed with bitumen.

What exactly is outside in the corner?
A photo of the outside view would certainly be helpful...

Photo 1 (77) is inside, the other shows outside.

How was the gap between the existing building (garage) and the new construction sealed from above?
That is a really sensitive spot.

We also had difficulties at this point (concrete carport is adjacent on one side to the masonry of the house) and it only got really good when the emergency sealing was done on the carport roof (flat roof). This was also pulled up the house wall to some extent. Attached are some pictures of how it was solved for us.

I can't show any long-term tests yet, but since this was done, nothing has come in anymore.

In your picture, which shows the outside, you can also see how the water runs down here.

Sorry, missed the photo. It looks like the water ran down the wall from the outside. That it then finds its way inside in the "raw state" of the wall (without plaster and base sealing) doesn't really surprise me. However, you also can't see the overall situation. Was there possibly a puddle outside in the corner (in the area of the cables)?

What exactly do you mean by base sealing?

Does the plasterer do this together with the exterior plaster?