A vapor barrier is intended to prevent moisture from the living space from entering the insulation so that it cannot mold.
Do OSB boards replace a vapor barrier? I have never heard that and can hardly imagine that OSB boards are vapor-tight themselves, but I am happy to be proven wrong.
There is still a difference between a vapor retarder and a vapor barrier.
Additionally, there is summer (warm outside = insulation warm) and winter (cold outside = insulation cold).
If vapor from inside (rather warm) reaches the insulation (when warm), not much happens; the vapor passes through the insulation to the outside and the insulation dries out.
If vapor from inside (rather warm) reaches the insulation (when cold), the vapor condenses and the insulation becomes damp/wet and cannot dry out afterward because of the cold. Mold can form.
The "climate membrane" seems to be the optimal hero here. When it is warm outside, it is "automatically" vapor-open (more like a vapor retarder). When it is cold outside, the membrane acts as a vapor barrier. In total, this means (at least theoretically) a lower risk of mold. As far as I know, a climate membrane costs less than one euro extra per m². Installation involves the same effort.
We have Intello Plus in our range. When I search online for climate membranes, I find many offers from Isover. I cannot evaluate either. Building material dealers can provide (dependent) advice here.
Edit:
Vapor protection is only necessary where vapor is generated (people) and the insulation must be protected.
OSB boards as flooring in the attic space have little impact here because they are installed above the insulation.