Remove tiled floor or lay parquet/vinyl on top?

so

Regardless of whether it works: The underfloor heating loses efficiency due to the additional buildup. With tiles on tiles at least I know that it works without problems, have done it myself before.

you mean tiles on tiles only with tile adhesive (so without leveling?)

you mean tile on tile with only tile adhesive (so without leveling?)

As an amateur, I didn’t level anything. It looked straight enough for me. I glued over it, no problems with the new floor. Also looks straight ;-)

In my opinion, that's botched. Bad for the underfloor heating and you lose some height. Floor tiles usually come up quite easily, I would quickly knock them out, that can be done in one day. You need leveling compound anyway. New doors coming? Otherwise, you would probably have to saw them off as well.

So now I have also spoken with 2 parquet studios (who also install parquet), a building materials dealer, and an acquaintance who is a floor layer. Opinions vary quite a bit!

V1
Remove all old tiles, new screed, then leveling compound, then parquet/new tiles
V2
Leave tiles on tiles and only work with tile adhesive, but for parquet remove tiles
V3
For parquet leave the old tiles, but clean tiles, decouple with decoupling mats, then leveling compound then glue parquet
V4
For parquet leave the old tiles, then level with leveling compound, then glue parquet

What to do now?!

Since our project is starting soon, it would be great if someone could share their experience on that... thanks :)

First of all, for answering your question, it is relevant how even the existing tiled floor is.
If it is completely even, then
- tile on tile only works with tile adhesive (done it myself)
- do not put parquet on tiles (not tried, it would be a shame for the good parquet if it doesn’t work due to slight unevenness or the tile joints)

I would remove the tiles. Then see how even the floor is, if necessary remove the remaining tile adhesive (sand it off).
If the floor is reasonable, then
- glue tiles directly (done it myself)
- glue parquet directly (done it myself)

Otherwise, work with leveling compound.