Exterior plaster is uneven, window sills are too short, tightness of the ETICS (External Thermal Insulation Composite System)

I do not assume that a client would accept something like that, especially not if they write about such an incident in a public forum. There will also be a chamber of crafts in his region :)

I always assume first that everything will be tried to avoid going to court. But a lawyer will also point out possible risks in his advice, at least that is what I would expect with an hourly rate of around 300,- :)

I do not assume that a builder would accept something like this, especially not if they write about such an incident in a public forum. There will also be a [Handwerkskammer] in their region :)

The [Handwerkskammer] does not do anything at all for a private builder. If anything, it only advocates for its members, which is usually the other side.

These are public-law chambers that list the experts, just like the engineering chambers.

By naming the TÜV, you are exactly referring to the organization that has business customers and thus also GCs as clients.
The difference lies in the public oath.

However, the technical perspective does not necessarily have to coincide with the legal one.

The TÜV expert was also commissioned and paid by the general contractor, but he really did not take a position for him in any respect, rather the opposite. You do not need a publicly sworn expert in the first step, because this will be appointed by the court later anyway. Besides, there are not that many of them and they have waiting times of up to 3 months. And if you commission a good one yourself, then he is "burned" for the court appointment, meaning he can no longer be taken. I have really dealt with this extensively.

Is a TÜV/DEKRA "Abnahme" part of the GU contract?

No. Unless explicitly agreed.