Solid wood parquet on underfloor heating

I haven't become poor because of that either :)

Nobody is saying that. But here and in other forums, people constantly optimize around the last unused kWh. Of course, something like the surface covering belongs in the equation.

Then only tiles are probably an option ...

I have laid tiles on underfloor heating in the hallway and layered oak parquet floating in the kitchen and living room. When wearing socks or barefoot, I notice that the tiles are warmer than the parquet. But only a little bit. And the thermostat is adjusted according to the room temperature; it is a comfortable 20°C everywhere. I find wood especially cozy. How much extra energy it costs me, I do not know. It is definitely great and I would do it the same way again.

Many years ago I rented a place with underfloor heating beneath parquet. It was never cold.

One must of course be careful with such statements as to whether it was an old underfloor heating system with higher temperature or already low temperature. The lower the supply temperature, the more insulation naturally has an effect. On the other hand, the low supply temperature is significantly more relevant for heat pumps than for gas heating. Also a factor to consider in the equation when searching for the perfect flooring.

On socks or barefoot, I notice that the tiles are warmer than the parquet. But only a little.

No, both should be equally warm. Only tiles conduct heat better and therefore feel warmer. In summer, it's the opposite, as the tiles simply feel colder.
It just takes a little longer for the heat to come through the parquet. Once it is warm, the difference in consumption compared to tiles cannot be determined by the average user.