Independent building expert - Necessary or alternatives?

4 appointments are too few. It has to be 10-14.

It would be 10,000€ at the TÜV just like that.

It would be about 10,000€ at the TÜV.

There are also many other regional providers who offer this in a package, for example for around 3,000€ net....

There are also many other regional providers who offer this in a package, e.g. for around 3 TEUR net....

How do I find them? Google?

Yes, search engine, phone book. Expert in construction / house building + location / district should already bring up something. Possibly also energy consultants; but they also tend to pitch their sales tactics. It depends on the local providers / in the surrounding area.

Or call a specialist lawyer for construction law to ask whom they would recommend...

The title "publicly appointed and sworn expert" is not necessarily important here - you are not yet in court / and do not want to go there right now. More important than the title is that the person on site is "on the ball," the "construction fox," and "gets along" with the craftsmen. Show-offs, fillers, phrase-mongers, standard-compliers, and dreamers are not needed here...

In the end, it remains a superficial visual inspection (therefore as many appointments as possible for each installation). Unfortunately, these guys do not have X-ray vision either, but they do have some measuring devices and, of course, experience.

Yes, search engine, phone book.
Expert in construction / house building + location / district should definitely bring up something. Possibly also energy consultants; but they tend to just run through their sales pitch. It depends on the providers locally / in the area.

Or call a specialist lawyer for construction law and ask who they would recommend...

The title "ö.b.u.v. Sachverständiger" is not necessarily important here - you are not in court yet / and you specifically don't want to go there.
More important than the title is that the person on site is "on the ball," is a "construction fox" and "gets along" with the craftsmen. Charlatans, filler, phrase mongers, DIN artists and dreamers are not useful here...

In the end, it remains a superficial visual inspection. Unfortunately, these guys do not have X-ray vision either, but they do have some measuring devices and experience.

My opinion as well, thank you for the tips. I think I will contact a few and then try to determine their competence based on the phone call and decide.

However, a general warning should be issued that it is especially a seller's or craftsman's market .... what good is it if you complain and the craftsman says he does this 150 times a year. The art will be to weigh when the expert is "exaggerating" and when you really should make a fuss ....

Windows are top with us, everything we complained about has been fixed.

The same goes for the shell builder.

The plasterer will still be difficult to get to fix things, some of it is out of tolerance, he simply has so much to do.

And the carpenter did not care at all about our complaint. Even the expert cannot change that.