The vapor barrier has a brownish position, insulation is wet

If you consider through which small pores of the membrane the moisture must have come in, almost 4-6 holes of size 10 on a 2.50x1.25 board should be enough

I don't think you can compare it like that. On one hand, there are diffusion-open films, e.g. roofing underlays, which offer almost no resistance to water vapor passing through. And that across the entire surface. On the other hand, you are looking at an OSB board with holes in it. The holes, in terms of SD-value, are comparable to a diffusion-open film, here about 0.02 m, while a film might be 0.1. But ONLY the holes. That means, if you have 0.1% hole proportion in the board, the film would still be 100 times more permeable.

You must not believe that moisture escapes convectively through the holes. No air flow establishes itself!

It may not be the best structure for this, but it is often done. If it were that problematic and done frequently, one would expect to read about more cases of damage. However, in reality, one does not read that much about it.

Don't understand the structure.
If after the insulation there's another layer of OSB boards, where is the moisture supposed to go then? Those things are practically airtight.

What exactly do you mean?

We have a house with a cold roof; accordingly, the insulation layer is not in the roof but in the top floor ceiling. The top floor ceiling is finished with OSB boards, which are necessary as a bracing panel and to be able to access the attic.

The climate membrane, which is attached from below to the beams in the living area, serves to absorb and release moisture from the living space depending on the situation. This works well in everyday life as soon as the house is occupied. In the current situation, due to all the construction water, however, it has absorbed too much moisture, which now needs to be remedied because the moisture was not removed quickly enough or because the vapor retarder was installed in front of the plaster and screed.

I also asked myself the question of whether and how the insulation layer needs to be ventilated in this construction, hence the idea of holes or slots, although it has already been pointed out here that this probably does not help, as no airflow is created and the water does not convect upwards through the holes.

Ah, I was in the attic, not on the top floor ceiling. If it is a cold roof anyway, I don't see it as that dramatic. However, the construction should actually have a vapor barrier and not just a vapor retarder. But as I said, in an uninhabited space it's not such a big deal, I initially thought the roof was insulated and was going to be converted.

I do not understand now why it should be less "dramatic" with a cold roof. The moisture still cannot get out of the "Zwischendecke". I don’t believe that the construction works like that. The drying process only takes place in summer. Regardless, after the screed everything first has to be opened up and dried. Depending on how many weeks pass until then, you might not yet have a mold problem.