Vapor barrier for parquet - yes or no?

We are currently dealing with our parquet flooring and would like to glue it down.

Now, you hear/read completely different things. Sometimes it is said that when gluing, you don’t need anything at all, then again it is said that you only need PE foil as a vapor barrier but no impact sound insulation, and then again both are assumed, especially on screed and underfloor heating, where at least the vapor barrier (PE foil) is often recommended.

With floating installation, it is clear that you cannot do without either. But what is really the case with gluing? Even the upholsterers have different opinions on this.

What is correct now?

Hi,
so our oak parquet in country house plank style was directly glued down.
That means first the screed was sanded and primed, then the parquet was glued. Of course, a measurement must be made beforehand to ensure that the residual moisture of the screed is not too high.

Otherwise, this is the first time I hear that a vapor barrier would still be required under a glued floor?