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

To get back to the topic, since you have now signed and all the lecturing is starting to annoy even me.

Your contract actually already answers your question:

 Excavation statics by the client
Note: for excavations of 4.00 m and deeper, a verification statics of the excavation is required - by the client
 Outdoor facilities, terraces, paths, parking spaces, etc. by the client
 Slope protections, shoring work as well as securing adjacent structures of any kind
by the client
 Demolition and removal or disposal of structural installations of any kind by the client
 Disposal of excavation material not required or not backfillable (see construction/
service description) by the client
 Expenses and services arising from requirements such as building permits, statics,
classifications according to earthquake zones and the like by the client

All expenses arising from the statics are the client's responsibility. In your case, of course, worst-case with the earthquake zone, but the risk is stated in the contract and you signed it as such.

yes, we knew that. we have budgeted 50000 euros for the things on the construction side

can I leave the offer as it is or can I somehow delete it again? because the name of the company is on it.

It’s best if you call your site manager once and ask for a meeting. Then you sit down together and you can discuss all your concerns/topics. Maybe solutions and ways can be found through a short channel to deal with it without immediately involving lawyers and experts. Maybe savings can still be found elsewhere. They naturally have many more options than you or we do. Even if it becomes unpleasant at first, constantly plunging into the unknown now doesn’t help either. If you run out of money in the end, it doesn’t help the general contractor either. Following the motto: "Honesty is the best policy." That’s usually the best way to go. Afterwards you will have a clear overview of everything and can understand all the problems in detail. And don’t sign anything without sleeping on it for 2-3 nights first! There are so many things to wait for during a construction project, so a few days won’t make much difference.

A good construction manager can also evaluate the [Nachtrag] for the basement [Weisse Wanne]. The [GU] won't be of any help there. Rather the opposite. He profits from the contract with the basement builder.

Someone who knows about construction law wouldn't be bad either, but that doesn't necessarily make it financially easier. Regarding the contract, the child is already in the well.

However, the specialist lawyer can still get the child out of the well, and the debt counselor can then dry it as best as possible.

(if you take out trades, the planned profit usually remains with the company),

That's exactly right. You put it very nicely and concisely, will you give me that as a maxim for further distribution?

they said otherwise they can't start with the work planning.

Waiver of revocation in exchange for prompt commencement of performance is a normal deal, it was just particularly unwise in your case – especially after the unanimous warning.

we were advised by the construction company to take out trades

The contractor doesn't care whether in the end you're left with a finished or only half-finished house when you run out of money. From their point of view, you may gladly accept an unfinished job. Whether you then save for twelve more years on the exterior plaster doesn't hurt them.

we don't have this in writing yet but as soon as I have it I will post it

You didn't "sign" the construction contract orally, did you???

We do have a site manager with whom we have been very satisfied so far

*ROTFL* before the first groundbreaking, he hasn't had the opportunity to make a bad impression yet.

that doesn't help me either – isn't the site manager responsible for site supervision?

Your site manager, yes, but not the one of your contractor. Their tasks are: 1. ensuring that no construction worker is left empty-handed due to late-delivered materials; 2. moderating between subcontractors; 3. effectively hiding defects until the warranty period expires. They have nothing to do with your interests, contractually you as the creditor of services are the counterparty!

A neutral site management/site supervision is included in the offer

That will mean that they get a seal of approval from one of the well-known vehicle inspection organizations, nothing more. I already recommended you an (online) course where you learn about such cheap tricks (?)

can I leave the offer as it is

Yes.

Maybe solutions and ways can be found informally to deal with this without immediately involving lawyers and experts. [...] And don’t sign anything without sleeping on it for 2-3 nights first! There are so many things you have to wait for in construction that a few days don't matter.

No, not a word more without the lawyer – and every hour you involve her earlier counts!

Maybe there’s room to save elsewhere.

If the contract can no longer be dissolved, it will and should in my opinion be the lawyer's goal to convert the house from 143 to 113 sqm. And, SCNR, you could have gotten that more easily as a "flair" (from Town & Country).

It says "Keller laut Plan" there. What does it say about the basement?