Which flooring to choose for the ground floor - experiences?

It has to be clear: The warmer a floor feels underfoot in an unheated state, the worse it conducts heat (that's why it feels warm) and is consequently less suitable for underfloor heating.

Basically, that’s also the conclusion of my half-sleepless night.
It’s a dilemma you can’t escape. You have the heating running half the year, during which the floor should conduct well, and the other half of the year it’s exactly the opposite.
I’ve also done some googling in the meantime and found several texts that clearly advise against cork for underfloor heating.
The intended floor would have had a cork intermediate layer of 2.7mm thickness, so thickness comparable to the wood layer of the parquet. That this should now mean a heating disaster seems hard to imagine, but anyway.

Well, what about the original idea and parquet??

I currently have parquet flooring in the kitchen. I don't find oil/grease so bad, rather that you have to wipe everything away and the dents caused by falling pots, knives, etc.

Therefore, yes, the question is what alternatives there are.

It's just a guess on my part. But when I already see in the apartment where it splatters everywhere while frying, I get a queasy feeling with parquet. And before anyone writes "just put a lid on it".... that doesn't always work.

Dents caused by falling pots, knives, etc.

How often do knives and pots fall on the floor for you? With pots, for example, tiles could also break, so that you have to replace them completely.
You could also lay down a transparent mat, like under office chairs. But whether you want that.

We will probably lay vinyl everywhere except for the bathrooms and utility room. In our current apartment, we have decent parquet flooring in the bedroom and vinyl in the office. My subjective feeling is that the vinyl feels much better. Parquet is noisy and (without underfloor heating) very cold. It will be fine with underfloor heating, but vinyl is probably less sensitive, especially in the kitchen. Parquet would be great - but I already know that we would have the “constant” re-oiling and sanding done. And if not maintained, it simply doesn’t look good.

There is a big difference between "patina" and "neglected." A well-maintained wooden floor inevitably develops a patina in the kitchen and gains character. You just have to know and like that.