First alleged fixed price and now additional costs - legal?

Here you have the lawyer, you just have to do what he advises you. By the way, I have asked several times what is in the payment plan and what has already been carried out.

The payment plan is: 3% upon submission of the GU's soil survey and the planning meeting. The planning meeting took place, but the GU's soil survey was not carried out. 7% upon handing over the building application 10% foundation slab etc.

Then offer them the 5% as the lawyer advised. Alternatively, you can of course continue building. But the fact that there will be additional costs is now known to you.

Considering everything mentioned here (reasonably not building), I would examine the financing of the additional costs. After all, it seems to be a very special situation.
Land paid for and equity available enough to finance the vast majority of the house. If now 50-70k€ should be missing, that would be a loan, depending on the land price, of around 30% or even less and a burden at 3% repayment and 1.5% interest of around 250€ per month. As soon as you live somewhere as a tenant, this position should at least be comparable, and if the 200k are saved independently and verifiably, there definitely seems to be potential, hopefully not "from earlier times and currently no longer possible."
Have you ever talked to your house bank, otherwise Volksbank or possibly Sparkasse to inquire, the situation is indeed special.
It is just an idea, even if the information given so far recommends withdrawal much more.

With everything mentioned here (reasonably not building), I would examine the financing of the additional costs. After all, it seems to be a very special constellation.
Land paid for and equity capital available enough to finance the vast majority of the house. If now 50-70k€ are missing, that would be a loan, depending on the land price, of about 30% or even less and a burden with 3% repayment and 1.5% interest of about 250€ per month. As soon as you live somewhere rent-free, this position should at least be comparable and if the 200k are saved up by yourself and verifiably, there certainly seems to be potential, hopefully not "from earlier times and currently no longer possible."

Have you spoken to your house bank, otherwise Volksbank or possibly Sparkasse, the situation is certainly special.

It is just an idea, even if the information given so far would much more suggest a withdrawal.

Thanks to you too for your suggestion.
For me, it is rather in the direction of "from earlier times and currently no longer possible." Therefore, I clearly informed the seller about my special situation well before signing the contract and wanted to ensure through constant inquiries about additional costs (including on-site inspection) that I could afford the construction and now these additional costs are supposedly unforeseeable.

I have also considered your suggestion. I can raise some money. I just do not know what "unforeseeable" costs the general contractor still wants to charge me, and easily an additional 30,000€ would already be serious.

Alternatively, the legal consideration remains. A law firm on the internet named "Ross**** & *****" with the keyword "Fertighausvertrag (Hausvertrag)" already offers some options there (Google search on the first page) that also relate to my case. The difficulty is that the general contractor is painfully careful to be able to deny any communication afterwards. That makes a later legal dispute difficult for me.

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Alternatively, there is still the legal consideration. A law firm on the internet named "Ross**** & *****" with the keyword "Fertighausvertrag (Hausvertrag)" already offers some possibilities there (Google search on the first page), which also cover my case.
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Is this turning into advertising?
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Then just offer them the 5% as the lawyer advised. Alternatively, of course, you can continue building. But now you are aware that there will be additional costs.

Thanks again for the help.

Well. The lawyer refers to the termination and he is certainly right there. But there are also other situations that relate more to my case. See "Fertighausvertrag (Hausvertrag)" (Google search) by a lawyer. However, proving evidence is difficult with a general contractor who is meticulously careful that communication is never legally binding.