Hello Maik, in my opinion not entirely without risk
what you are planning there!
"The structure of the ceiling is panels (on battens) - straw clay plaster - cavity - floorboards.
I initially thought that the cavity between the floorboards and the clay plaster would be filled, but according to a company, the attachment of the clay plaster is not stable enough.
I now wanted to apply something on top of the floorboards."
The construction seems critical to me especially because the ceiling of a heated living space borders the unheated floor below. The company might well be right with their statement, but the cavity can also contain so-called "inserts," which then serve as insulation carriers. The underlying ceiling structure is then completely decoupled and not additionally loaded. It could also use very light loose fill, so that an insert such as gypsum board on battens can be used instead of thin tongue-and-groove boards.
But since you want to save yourself the work of removing the floorboards, you basically only want to roll out "mats" or similar as insulation on top. In my opinion, that would shift the dew point into the floorboards: Warm air rises from the living space upwards, passes through the panels, is stored depending on the thickness of the clay plaster, what cannot be stored floats further upwards and accumulates in the cavity (convection). Without insulation, the remaining heat draws through the floorboards and then through the uninsulated roof. With insulation, the air condenses below the insulation, presumably mainly on the underside of the floorboards in the cavity. There, in my opinion, dew water forms and possibly damages the entire wooden structure.
The use of a vapor retarder is recommended by the manufacturer when mineral wool is used. Laying the foil on the floorboards would, in my opinion, only change the above scenario so that the wool is protected from condensation moisture, but not the wooden structure. A vapor retarder is placed on the warmest side, so for ceilings below the insulation. The "on-floorboards insulation" option is, in my opinion, excluded due to the critical design. Especially in winter, when warm air of 18-20°C enters the cavity below and then slowly cools down by 15-20°C, a considerable amount of dew water is likely to form. The insulation laid on top slows the cooling but does not prevent it.
In my opinion, all possible solutions require removing the floorboards and correctly insulating the cavities. Suitable options, in my opinion, are mineral wool solutions with vapor barrier foils underneath and around the beams or various solutions with loose fills. As far as I know, with sufficient loose fill thickness of perlite or similar, a vapor retarder can be dispensed with because the warm air rising through convection produces just as much dew water in the insulation, which can be stored harmlessly by it and later released again. For that, there are smart gypsum programs and engineers who can calculate this exactly.
I am not a building physicist, but I have been dealing with the subject in theory and practice for years. I therefore hope not to be too far off with my explanations.
Regards