Parquet on underfloor heating without basement - floating with vapor barrier?

First of all, it is such that all manufacturers of floor elements, whether multilayer parquet, laminate flooring, or another click system with MDF or HDF carrier layer, generally prescribe a vapor barrier between the subfloor and the "Trittschallfolie".
One does not have to do this, but then one is "on thin ice" at one’s own risk. If there is later a reason for complaint, logically the flaw will be found in the form of a missing vapor barrier and used as a refusal of a complaint that might be basically justifiable.
Technically, however, it is such that with cement screeds, both with and without underfloor heating, it must be considered that cement screeds absorb moisture starting at a relative humidity of about 70%. This moisture is absorbed by the screed structure and is released again faster with underfloor heating and slower with conventional screeds.
However, according to the physical principle of water vapor diffusion equalization, the moisture contained in the screed structure moves toward the room, which has a lower water vapor partial pressure (in this case the room air above the floor covering). This moisture is stopped at the interface between the floor covering elements and screed and then hits the carrier material of a wood-based floor. That tends to swell and leads to unmistakable features on the surface of the covering. To put it mildly.
A vapor barrier would then have the task of reducing the passage rate so that the moisture, as far as it is absorbed by the carrier material, would be released very slowly and unnoticed to the room air.
That is why the PE foil, as far as it has a vapor diffusion factor (that is the sD value) of over 80, is called a vapor barrier!
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I hope I have expressed myself clearly and unambiguously here for everyone, not just for electrical engineers (FH).
Regards: KlaRa

We also installed the vapor barrier under the floating vinyl. The painter’s specialist company (a friend of a colleague) came by once and mentioned that we could have sourced the floor through them as well. Regarding the vapor barrier, he seriously asked what it was and said they had never sold/installed it before. I was initially unsettled by that. I understood that this PE foil as well as the floating installation are worse for the efficiency of the underfloor heating. But I didn’t want to take any risks. So far, I haven’t noticed anything negative. The foil was even helpful during installation, as it made the floor easier to lay.

“I was aware that this PE foil as well as the floating installation are worse for the efficiency of the underfloor heating.”
Response to this:
The thermal resistance of a 0.15mm thick PE foil is so low that it can be practically neglected in heat transfer!

I have now chosen the Knilchen version, am installing impact sound insulation with integrated vapor barrier, and am also extending the vapor barrier 3cm up the wall.

Thank you for the help and explanation!