Heat pump is not compatible with a water-bearing fireplace

Well, with any heating system, I would still expect to be able to temperature my individual rooms differently. Who wants the same temperature in the bedroom as in the bathroom.

That only works to a limited extent and within certain boundaries. Efficient it is not at all.
Basically, the same tempered water runs through the underfloor heating in every room. You only regulate the amount with the flow in the heating circuit distributor and at the ERRs when the heating circuit is closed. There is no such thing as 24 degrees or 20 degrees to the tenth decimal. If you want 24 degrees in the house, then 37-degree warm water runs everywhere through the floor. It just has to be brought to 37 degrees. Which takes a long time in winter at 0 degrees. The colder it is outside, the longer it takes. Therefore, a low temperature in the house is efficient, because the heat pump does not need as long.

The client who is now building anew often does not even know the difference between convection and radiant heat. He comes from an apartment with radiators and then has to realize how different the underfloor heating heats.

I think this is the real problem. People rely on someone, here probably the architect, without informing themselves in advance.

But not everyone likes it. Personally, I don't either. I always have warm feet and I don't like this constant heat from below. It is said to also promote the formation of varicose veins and similar. So underfloor heating is not always advantageous for health.

It's good that there are different preferences. I like that I have the same temperature at 2 cm height as at 170 cm and also at 380 cm. So I'll get laughable varicose veins?

This is only possible to a limited extent and within certain boundaries. Definitely not efficient.
Basically, the same tempered water runs through the underfloor heating in every room. You only regulate the amount with the flow in the heating circuit distributor and at the ERRs when the heating circuit is closed. There is no such thing as 24 degrees or 20 degrees to a tenth. If you want 24 degrees in the house, 37-degree warm water simply flows through the floor everywhere. It just has to be brought to 37 degrees. That takes a long time in winter at 0 degrees. The colder it is outside, the longer it takes. That is why a low temperature in the house is efficient, so the heat pump doesn't need as much time.

Then you should get a heat pump, that works.

Then you should get a heat pump, that makes it possible.

I have a heat pump :) the target return temperature is 25.5 degrees, however the heat pump has to heat the water to 33 degrees until, with a spread of 2 degrees to the actual return temperature, the heat pump switches off and the screed maintains the room at 21.5 degrees. The target return temperature is not the water max temp, but the max temp of the screed that brings the room to 21.5 degrees.

I have a heat pump :) the return temperature setpoint is 25.5 degrees, but the heat pump has to heat the water to 33 degrees until at a differential of 2 degrees it switches off and the screed maintains the room at 21.5 degrees.

OK, that's just how it is when you first heat water with loss and then pump it through the screed. It also works without the water and the heat pump only heats where it is necessary in the room.

Not everyone likes it though. Personally, I don't either. My feet are always warm, and I don't like this constant warmth from below. It is said to also promote the formation of varicose veins and similar issues. Yep. Supposedly promotes varicose veins. I've also heard that the Earth is supposed to be flat. Medically, the myth is just as debunked as the flat Earth myth has been settled. That's just bar talk.

And this constant warmth is nonsense as well. At least in new buildings. Currently, the heat pump is running (at 6-8 degrees at night and 13-14 degrees during the day) at about 26-28 in the new building (with a 5K spread). That should result in a floor temperature of about 22-23 degrees at a room temperature of about 21-22. I measured it myself. Depending on the room, just 22-22.5 degrees floor temperature. That feels anything but warm. It won't be much different in deep winter either.

P.S. The relatively high supply temperature (!) results from the fact that I currently have an unheated floor above my entire apartment (two-family house). I naturally heat that through my unit as well. Upstairs it is only 17.5-18 degrees.

If you want 24 degrees in the house, 37-degree warm water runs everywhere through the floor.

If that happens in winter, you either live high up in the mountains or a nail stylist planned the heating ;.)