How much additional cost according to the structural engineer's calculation?

They said they can't start the planning otherwise.

No one can tell you that without context. I only know that disposal is currently extremely expensive. We spread all our soil work on the property because disposal is too expensive for us. We were given a figure of 400€ per truck trip, and that doesn’t even include the landfill, just the transportation. And in the context of basement excavation, it’s more than manageable what fits on such a truck. Can you store it somewhere on the property? If not, can you still repaint the basement? I don’t think it was planned properly. If no sealing was included, and you didn’t factor in soil disposal / earthworks, it could blow your budget.

Do you perhaps mean the statutory right of withdrawal?
That would be something different. Waiving it so things can get started, I think, is not uncommon.
Did you have any alternative offers so that a withdrawal might make sense? What you have told us so far seems a bit wishy-washy to me. Although we don’t know many details either. Maybe you can enlighten us a bit more.

Unfortunately, only one drainage was planned for the basement, which unfortunately, according to the soil report, does not work.....

Unfortunately, we can no longer paint the basement because otherwise, we would have to start all over again.

Yes, that would still be an idea to store the earth on the property.

Regards

A basement with drainage, in my opinion, should not be built anyway. A basement always requires some sort of waterproofing. Or a white tank. But that is even more expensive. What exactly does the offer say about this?