You probably mean Styrodur or PS20 Styrofoam,
but in my opinion something like that belongs under a screed concrete floor on the ground floor or a floor slab. Rigid foam does not allow moisture to pass through and would cause condensation problems in the timber framing again, so in my opinion it is unsuitable for your construction.
"Seeing it differently, the problem now arises in the cavity between the beams, is that correct?"
I already answered that in the first post:
"Without insulation, the residual heat escapes through the floorboards and then through the uninsulated roof."
In addition, I would say that with the current uninsulated solution, no condensation problems should occur.
Yes, if you now directly ask me about the vapor barrier solution ... I myself am absolutely against bags and foils in the house, especially in old buildings. But in new construction I also had to insulate against my attic like this back then, whereby in my opinion I minimized the risk:
My first solution was: gypsum plasterboards from above onto the beams (which should be "rustic" in new buildings), then vapor barrier tacked over everything from above, then battens screwed from above onto the beams, gypsum boards then screwed from below through a stop on the battens. Then mineral wool applied seamlessly on top and done. The dew point was thus located in the gypsum boards, which absorb and release a little of the normal condensation moisture or simply let it through. The system enclosed no wood, because the beams were underneath, the battens on top.
With non-visible beams I first tacked the vapor barrier taut and well overlapped to the beams from below, then the battens from below and gypsum boards on top of them. From above then the mineral wool between the beams. Here only the battens (impregnated) were below the vapor barrier. Moisture could therefore not penetrate into the beams. For 9 years I have had no problems with either the first or second construction so far. The attic is insulated in the slopes but of course not heated.
For you both solutions probably do not come into question because you certainly do not want to tear down your paneled ceiling on clay plaster. If you also want to keep the floorboards, then I would do nothing. But you are now considering lifting the floorboards. Therefore my very personal suggestion for how I would proceed in such an old building:
Unfortunately remove the floorboards, check the beams, are they all okay? If you have the chance to open it up, you should check that at the same time. Then see whether there are already inserts in the ceiling (so-called "Schwartenbretter") with clay / straw / rubble / empty beer bottles on them. If yes, the demolition could be stopped. If the dirt on the inserts is not wet and too moldy, I would leave it in. It also provides insulation, thanks to its mass also decent sound insulation when the floor is later expanded. If there really is nothing between the floorboards and the ceiling, screw impregnated battens as deep as possible on the side of the beams (upright), then inserts made from gypsum boards or thin tongue-and-groove wood on top. Pour loose-fill insulation on it, possibly with trickle protection underneath, but no plastic foil! Best to build the inserts so cleanly that no gaps arise. Fill the loose fill up to nearly the top edge of the beams (at least 20 cm would be good in my opinion). Then leave the floor open, lay walk boards on top and that’s it.
If the floor remains unheated, moisture may rise that can no longer be stored by the insulation and pass unhindered upwards and penetrate the roof. In my amateurish opinion, no vapor barrier would be necessary in this case. If the floor is later developed, it will also be heated. Between two heated storeys gypsum creates little vapor pressure gradient so that in my opinion a vapor barrier is also not necessary. But please install floorboards and no toxic OSB or chipboard! Those things can act like vapor barriers and cause moisture to condense on the beams unnecessarily. Normal diffusion-open coated floorboards, in my opinion, let moisture pass. One should not place unnecessary obstacles in the way of convection.
Regarding the insulation material: I advise against any kind of "bio insulation". This stuff is usually impregnated with insecticides so that insects and other critters do not eat it. Cellulose is also not without problems in my opinion because it is treated with toxic borates. I trust expanded clay and untreated mineral perlite, so nothing biological.
Maybe you better discuss this beforehand with someone who can call themselves a "building expert" and see what they think of it. I am also interested in factual criticism.
Regards