Is a vapor barrier necessary under insulation on a floor slab?

Yes, it's not quite easy to get decent photos. So the bright area at the top is the insulation, clamped between the wooden beams running across the picture. At the front top of the wall there is this groove, where I am not quite sure yet which material I should best use to fill it. Because exactly there, as high up as possible, where the empty groove is now running, I would like to connect and seal the vapor barrier airtight.

Then the battens will be installed perpendicular to the beams.

So I think you can then fill the joint with [Stopfwolle] in a material-appropriate way.