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

Quote Wikipedia: “Als Schwarze Wanne is the waterproofing located in the ground made from bitumen thick coating, bitumen or plastic sheets, when it completely encloses all earth-contacting components of a building in a (pressure) watertight way. With proper execution, the schwarze Wanne can be used when the basement rooms are below the groundwater level.”

Yeah, I've been going on about that since page 1.

and what do you think I should do? cancel the contract somehow and pay just as much elsewhere? we need a waterproof shell anyway in zone 3 and we also need 140 sqm of living space

what use is "what you need" to you if you can't afford it. it has been written often enough what you should do. get professional support. they will then tell you what options you have. in the worst case, you end up with a half-finished house. maybe it would be best to cut your losses, somehow get out of the contract with a little lesson learned and start over with a reputable provider based on your budget. and if it then doesn't include a basement and 140 sqm, then so be it. but only someone who professionally examines your contract can judge that.

we are in the west. ok, 550000 and that does not include additional construction costs like, for example, earth removal?

The rough calculation is 3000€/sqm = 450k, 100k for the basement and 50k for additional construction costs. That can work, but it doesn't have to. With a basement, 50k additional construction costs are rather tight; you would then have to come out correspondingly cheaper in terms of living space. That in turn can work, but it doesn't have to. You won't get a detailed breakdown accurate to the thousand by remote diagnosis anyway. You will have to find a suitable professional and go through your contracts, the building specifications, and everything else with them. This far exceeds what a forum can provide on the side, and besides, we do not have the complete documents either.

What is that supposed to mean? You have a signed contract and still no expert at your side. How do you want to be able to evaluate another offer?

Exactly. Moreover, it is an absolute waste of time to get an offer when you have already signed a contract with another provider. You can use that time more sensibly and, as often recommended here, get in touch with a lawyer.

But, and 11ant has already written this too... if you can no longer manage 20,000 EUR now, it will not be 140m² with a basement, but rather 140m² without a basement and with a lot of own work in the current situation (high construction costs, high interest rates)... or only 120m², but without much own work...

I can tell you how I calculated: The sample calculation said 420,000 EUR. I first made it 450,000 by increasing some items so that the bank would lend us a bit more money. And then we also held back a good 70,000 EUR from our equity. Our reserve was therefore 100,000 EUR... and what can I say...

The house is standing, we live in it... but the reserve is gone. And we don’t have a basement, especially not in earthquake zone 3, and we were able to use all our excavation on our property. That’s a lottery ticket... if the soil is even slightly contaminated, then God help you...

and what do you think I should do? cancel the contract somehow and pay just as much elsewhere? we need a white bathtub anyway now in zone 3 and we also need 140 sqm of living space

You should - but I have said this several times already - clarify your situation with the specialist lawyer, get advice from her, and then proceed based on the facts. In my opinion, this will inevitably involve responding to the excessive costs by reducing the size of the house by probably about 30 sqm. Burying your head in the sand and hoping for an apparition of Mary is not, in my view, an effective course of action.

This attitude is regrettable, unwise especially for your work, and not a good influence on the OP. Legal advice does not mean a lawyer's call or a lawyer's letterhead. And lawyer does not mean confrontation at all. I appreciate the mentioned specialist lawyer as capable of successful mediation, and the OP should of course also respond covertly with advice – for example, sending the contractor a letter formulated by the specialist in her own name. Don’t scare the OP into fearing escalation!

Well, what is wise for my work I can probably decide best myself ;)

Generally, from experience, I have fared best privately as well. In every respect. I am currently building my first house and fortunately have no problems, but that is exactly how I would approach it there as well.

At the end of the day, we can all only offer advice. The OP must then decide for herself what she feels most comfortable with, but please try not to be so disparaging; that usually achieves the opposite.