The construction company is building a basement smaller than in the factory plan

My expert measured the concrete cover. I hired him specifically and only for that purpose, when I noticed the defects after the formwork was removed from the basement walls. I did not commission a remediation plan.
The letter equating "a black tank with a white tank" was presented as a response by the construction company. It comes from some in-house "structural engineer" of the construction company (he did not calculate anything on my construction site).
However, construction is carried out according to the architect’s plan (shop drawing) and reinforcement plan/structural calculations (by "my" structural engineer) that I provided.

Now things become a lot clearer.

Allow me at this point to ask you directly why you did not clarify this in the original thread and effectively “stopped” communication there?

I expect the assumption of consequential costs (e.g. adjusting the execution plans) and a price reduction. I am interested in how much money is involved (court rulings or similar).

Here again for understanding: Your expert certified the defects but did not provide any assessments as to how these defects render the building unsuitable for the soil conditions? Then you should clarify this here, because what use is a basement free of charge if you can only use it annually as an indoor pool? Find out whether the basement is suitable at all or can be made suitable and only after answering this question should you consider whether to pursue damages or rather demolition.

In verbal discussions he denied all errors.
Only after the evidence from the expert (concrete cover) did he respond and only conceded those defects described by the expert.
He still denies dimensional deviations.

He will deny everything that is not presented to him by the expert. That is the reality—unfortunately. One could discuss price reductions concerning the measurements if no serious disadvantages are to be expected. But that requires the other issue to be resolved first.

Do you see yourself able to settle this without an expert (who covers both issues and possibly more) directly with the builder? Have you taken out legal expenses insurance for builders? A telephone consultation with a specialist lawyer will cost you less than €200. If an expert confirms both defects to you, I would also involve a lawyer in your place; only they will put your claims into legally impeccable form.

Allow me at this point to ask you directly why you did not clarify this in the actual thread and effectively "stopped" communication there?

My question in the thread about concrete cover was of a technical nature: which variant of the renovation to prefer. The answers went in a different direction.

Here again for understanding: Your expert certified the defects to you but gave no assessments as to how these defects make the building unsuitable for the soil conditions? Then you should clarify this here, because what use is a cellar to you for free if you can only use it as an indoor pool every year? Find out whether the cellar is even usable or can be made usable and only after answering this question should you think about compensation or possibly demolition.

The expert did not provide written assessments but communicated that the cellar can be renovated and the builder should do it. One should agree on the appropriate variant.
The cellar can be made usable. But a black tank is of lower quality than the ordered white tank (not as durable, etc.).
And it is smaller than ordered. Additionally, the wall to the neighbor cannot be inspected (renovated from the outside).

He will deny everything that is not presented to him by the expert. That is reality - unfortunately. Regarding the dimensions, one could, if no significant disadvantages are to be expected, negotiate price reductions. But that requires that the other issue is clarified.

Do you see yourself able to settle this with the builder without an expert (who represents both issues and possibly more)? Have you taken out builder’s legal expenses insurance? A telephone consultation with a specialist lawyer won’t cost you 200€. If an expert confirms both defects to you, I would also hire a lawyer in your place; only he can get your claims down on paper in legally impeccable form.

I want to try to settle this with the builder without an expert.
Is the burden of proof on him if I officially complain about something in writing? Or can he simply reply "no, the dimensions are correct"? I want him to bear the costs of proof himself.

I see all the ingredients here for a new Fleischerhaus given. A construction company with no knowledge of the trade and no quality control. A client who saves in the wrong place, only hires an expert for defects already identified, and hesitates to take a specialist lawyer.

I am asking whether you have already put the basement builder on notice in writing to remedy the defects with a deadline. You seem to be managing the construction supervision yourself. Otherwise, the site manager would take care of it.

Request a remediation proposal from the basement builder regarding the defective concrete cover that ensures equivalence of the components. I will inquire again. What does the contractor owe according to the contract ([Weiße Wanne])?

In case of deviation in the dimensions that do not comply with DIN tolerances, you or your site manager have violated the duty of inspection. You as the client bear some contributory negligence.

Nevertheless, I would also ask the contractor for a proposal to remedy the defect, with the recommendation to report the damage to his insurance.

If you have time for a lawsuit, definitely get advice from a specialist lawyer for construction law. He should also be able to handle the professional correspondence. The contractor will laugh at you if nothing solid comes from you.

If at all, only pay for the basement partially and under reservation at first.

I want to try to settle this with the shell builder without an expert. Does the burden of proof lie with him if I officially complain about something in writing?

No, why should he have the burden of proof? And what exactly do you mean by "officially complain about something in writing"? Then the shell builder just says "sorry" and that's that.

called on the basement builder in writing to remedy defects with a deadline

That would be the bare minimum here. But then the shell builder just does his coat of paint and that's it. Is that a correct solution? No one knows. He will refuse to enlarge the basement due to disproportion.

I want to try to settle this with the shell builder without an expert.

Both threads should have shown that this is a really stupid idea. It's about way too much money. And please don't take it the wrong way, but you don't make a good impression trying to handle something like this yourself. Just the question about the basement builder's burden of proof makes my ten toenails curl. Once again, very clearly: consult the expert on construction questions to help find a solution.

I want to try to settle this with the shell builder without an expert. Is the burden of proof on him if I officially complain about something in writing? Or can he just reply "no, the measurements are correct"? I want him to bear the costs of the evidence himself.

Measure the basement together with the construction manager / foreman of the basement builder. Have the protocol countersigned during acceptance. Of course, reject it due to defects. Announce the costs in advance and withhold them. I would also deduct the costs for measuring the reinforcement position from the contractor.