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

It can't hurt to insulate the suspended ceiling

Yes, but more in terms of sound. And as I said, if the roof insulation is done, you should also heat/ventilate there. Possibly less than if people were regularly staying there, but moisture does get in, which then cannot get out.

I would probably rather not install a vapor barrier so that the moisture can at least get out again, but at the same time set up at least one hygrometer with a transmitter/receiver there and mount the display in a place where I pass by regularly.
But you have now written to the EB, I'm curious to see what they reply...

No, no ... regarding heat ... the gable wall is (still) not insulated and he said, before the heat escapes through the attic, just insulate the top living floor if the ceiling is open anyway.
You mean ventilating because the roof is being sealed and the air can't escape? I understand ...
But why heating? The room will initially only be used as a storage room or something similar ...

If you don't heat there, the room will of course cool down despite insulation. When it's cool, the air's capacity to hold moisture decreases. So the dew point moves closer to the room temperature. Eventually, moisture condenses and cannot dry out due to the airtightness. Constant moisture conditions are a medium-term mold problem.
Search for dew point calculators; it’s quite quick.
For example, 50% humidity at 21°C is already over 80% relative humidity at 12°C.

Smaller problem: If you don't heat there, you end up heating the roof from the upper floor (at least if you don't insulate the floor now or only a little).

Ah yes, I understand, thanks for the explanation. I can already tell that it’s more towards a vapor barrier - oh dear, I’ve gotten myself into something :)

Well, not necessarily, if you go up there rarely but regularly, you do bring in moist air. If you are diffusion-tight all around, the moisture can't get out. So from my point of view, it becomes even more important to heat/ventilate. In the end, the energy consultant has to say, but I would guess: with ceiling insulation, pay more attention to soundproofing (not maximum thermal insulation), for example wood fiberboards, keep the entire construction as diffusion-open as possible, and some type of minimal heating that kicks in as soon as it drops below 16° (split air conditioner?). Or just ventilate up there regularly (decentralized ventilator with heat recovery), preferably both.

I am also concerned that all the moisture does not penetrate into the mineral wool and remain there. If it then moves upward into the attic, that would still be okay, because then the problem would be solved by regular ventilation according to my understanding. That would be feasible (or just install decentralized ventilation, as you already mentioned).

With a vapor barrier, most of the moisture would stay in the living space and wouldn't reach the mineral wool at all – then you could simply ventilate the living spaces (which you do anyway) and everything would be fine ...