Vinyl in floor-level shower

You’re away for a few weeks... and then there’s this nonsense up there with the urban legend about wood and the poor conductivity of air... help... that has hardly anything to do with the effects of underfloor heating. An underfloor heating system works only to a small extent by convection. That’s exactly what makes it so pleasant...

Apart from the usual prejudices... laminate is for welfare recipients, vinyl is middle class, parquet is above all questions... tiles naturally depend on the price, at 25 EUR/m² you better not invite anyone, you are only allowed to show the rooms starting at 40 EUR/m², be sure to keep price tags(!)...

The effort and costs for sanding parquet flooring are absolutely comparable to those of a new installation. The room must be empty, baseboards must be removed, sanding, filling deep spots, oiling... It can be cheaper to install engineered parquet and just throw it out and replace it after 10 years. You can do it yourself, it can be floating. I installed it floating in a 4x10m room, with a 15mm gap on the short edge, 10mm on the long edge. No problems. What I was told: "No! You never install parquet floating, that ends in disaster!..." Now the third summer is approaching, the parquet is there, it looks good and cost me 50 EUR per m², plus my labor. When the children are older, it will be taken out in 6 or 7 years, engineered parquet will go back in for 50 EUR/m²... and I’m still cheaper than a specialist who had the stuff glued for 120 EUR/m² and then after 10 years has it sanded, filled, oiled, etc. for 90 EUR/m²...

At least I was able to convince my wife to tile the bathroom.

Very good decision! There is also the opportunity to design the bathroom as its own highlight. In particular, this creates an exception to the otherwise continuous wood look. As for the rest of the house (but I wouldn't do this in the bathroom): there is higher quality vinyl with a reasonable wear layer, high abrasion class, and waterproof joint. Especially with pets, I would pay attention to that. Regular vinyl, on the other hand, can quickly look really worn out with pets. However, if I had the choice and the financial means between that or tiles/wood flooring, I would always choose tiles/wood flooring.

A floor heating system works only to a small extent by convection.

Do not quote out of context, it was about the cooling function. There is no radiant cold. Air does not emit heat by radiation. Air warms (transfers heat to a body) by convection.
And what are you trying to say anyway, your entire tone is critical, but in the end do you recommend parquet or not?

What does it look like if the cat pees on the parquet and it is not discovered right away and soaks in nicely? Our cats are unfortunately such candidates. But in general, one should consider that, because old animals like to pee everywhere. My wife is very opposed to parquet and wants click vinyl because of the cats. Our contractor also asked us if we are planning parquet somewhere, because then a different height would have to be planned for the screed.

How does it look if the cat pees on the parquet and it isn't discovered right away and soaks in nicely?

The question is how good the protection of the surface is. Lacquered or oiled. Re-oiled or unmaintained. With lacquered (there are also matte lacquers), you have very many hours without any problem. Oiled (Haro parquet from experience with a dog) at least a few hours without anything happening.

My wife is very opposed to parquet and wants click vinyl because of the cats.

It is a mistake to believe that the joints are 100% sealed. The urine finds its way through the click parquet. In combination with underfloor heating, this is a room scent that at least does not meet my preference. Given these requirements and the available budget, foregoing tiles is purely functionally difficult.