The vapor barrier has a brownish position, insulation is wet

Well, simply because you don't have mold in the living space then. Normally, the insulation of the ceiling above a vapor barrier. Letting moisture diffuse in and then sealing it from above is simply nonsense. In everyday use with drywall panels, that might be minimal and work, but it is never smart.

Why is it different with the top floor ceiling than with the roof? In principle, nothing changes here. The cold roof basically "only" protects against rain and wind.

Whether a vapor barrier is better than a retarder or a membrane, well. As far as I know, the trend today is to move away from barriers towards retarders or membranes. It has generally proven to be better if there is some space to work with.

The same "problem" is often found in wooden houses as well. Inside, the OSB boards serve as a barrier/retarder and outside, after the insulation, OSB boards are also very often used. Basically a "stupid" construction because moisture that has penetrated can neither escape in one direction nor the other.

What might not have been wrong is the bracing layer not after the insulation but before the insulation. Then, for example, one could work with tongue-and-groove boards after the insulation. These are laid with a "good" gap dimension and preferably only where the attic is to be accessed or something stored. Whether that is feasible in each individual case would have to be clarified or could have been clarified.

Well, simply because then you don't have the mold in the living area. Normally, the insulation of the ceiling slab is placed over a vapor barrier. Letting moisture diffuse in and then sealing it from above is simply nonsense. In everyday use, when covered with plasterboard, it might be minimal and work, but it is never smart.

Sorry, I don't understand. With insulation in the converted attic, the mold would not be in the living area either, but behind the membrane. Otherwise, Garfunkel is right.

To make it short:

Vapor barrier for e.g. [Hinterlüftetem Dach] or in the floor slab.

And everywhere moisture cannot be discharged to the outside, a climate membrane/vapor retarder is used to release the moisture into the room. The membrane including insulation should only be installed after the construction drying has been completed and no further moisture ingress is expected.