Air-water heat pump combined with underfloor heating does not work properly

It is indeed confusing when the room controllers are labeled in degrees Celsius. Such a system cannot provide that at all. I think that is already the fundamental misunderstanding.

First of all, most of the described observations are indeed normal for a modern heat pump with surface heating (underfloor heating). Furthermore, for an efficient operation of the heating system, using individual room control is rather detrimental or superfluous. Actually, you would set the desired temperature directly with the heat pump and the valves on the heating circuit distributor, which is then maintained. Strongly different temperatures are not or only poorly possible, because everything within the same thermal envelope heats each other up.
Bathrooms are often typically cursed by their limited area and the higher heating demand with an undercoverage of the heating capacity. That’s why additional heaters are often planned. However, it only makes limited sense with low-temperature systems to integrate these into the "normal" heating circuit, since it runs with low temperature. You therefore need a large surface to achieve effective heating performance here. It is better to use electrically operated radiators for this. These exist classically as towel radiators. You can check (have checked) whether your towel radiator can accommodate a heating cartridge. This is then inserted, for example, at the bottom of the towel radiator and connected to a power outlet. Converting this is, of course, no longer so easy and should be done by a professional company.
Alternatively, you can look for other heaters. There are stylish infrared panels or the not so beautiful ceramic heaters. Or, for example, quite classically fan heaters.

So, does that mean I cannot individually control the temperature of every room? If that’s the case, I find that very bad. What use are temperature controllers in every room then? And why did it work that way in our apartment? Could it possibly be due to the connected district heating?
We have towel radiators with heating cartridges that are plugged into the socket. However, I also don’t find it really good to compensate with that. I do wonder whether this investment was a total wrong decision.

Well, from the statements in the initial post, I can deduce that there are no errors. The heat pump does what it should and exactly as it should.

You can disregard the controllers in the rooms. They are just wall decoration. Or rather, they can function as an emergency brake. But then you would have to run your heat pump higher than necessary, and who wants that.

The behavior you describe is exactly how a heat pump should function. In your apartment, you probably had underfloor heating that was not heated by a heat pump, which also explains your surprise that it worked there but not in the house. Am I right with this assumption?

You are right regarding the apartment. It worked there because district heating was connected?
Regarding the emergency brake, however, I also could not detect it when the desired room temperature was set to 23 degrees. Although the temperature controller indicated no heating, we had between 22-23 degrees with the window open, meaning the underfloor heating was still active, even though we had not set it.

It is indeed confusing when the room controllers are labeled in degrees Celsius. Such a system cannot provide that at all.
I think that is the fundamental misunderstanding already.

Unfortunately, no one explained that to us. However, the analog controllers also show the degree numbers. We also had that in the apartment.

So this means I cannot individually control the temperature in every room?

No, but firstly not by more than 2-3 degrees difference, secondly always only with efficiency loss, because adjacent rooms that have a higher desired temperature heat the other room as well.
Secondly, with an efficient system, you do not change the desired temperature daily on a (poor) control, but rather design the heating system for the desired temperature from the start. This also includes, on one hand, determining the volume flow and the installation spacing at a predefined flow temperature, which should be kept as low as possible.

If that's the case, I find that very bad.

Your construction company or heating installer simply gave you poor advice or just did the bare minimum.

Then what use are temperature regulators in each room?

Nothing, but they are legally required, and exemption seems complicated and unlikely, though possible (according to reports here in the forum).
Ultimately, the recommendation here is to either ignore the ERR (individual room control) (set permanently to maximum), or even deactivate it by unscrewing or disconnecting the actuators at the heating circuit manifold (if power is off: set to open).

And why was it possible in our apartment then? Could that possibly be due to connected district heating?

More or less. District heating water arrives at 70-90°C at the heat station in the building. That means the flow temperature at your heating circuit manifold is still at least 60°C. With that you get the floor properly warm, and at full flow it’s actually already too warm.
Currently, in my condominium, I have regulators that show 5 levels but basically only know on and off. That means, if I turn it on, it actually gets too warm during transitional periods, and I adjust several times daily or just have full heat in the bathrooms and only heat the other rooms as needed.
Since the heating water is already so hot, efficiency is not high anyway, and the loss remains within limits.

We have towel radiators with heating cartridges plugged into the socket. However, I don't think compensating through that is really good either. I wonder if this investment was a total mistake.

No, that's exactly how it’s done. The short-term additional heat demand must be supplied electrically. Raising the system’s entire flow temperature and then throttling the volume flow in all rooms except the bathrooms will cost you much more in the long run than running the heating cartridge for 15 minutes in the morning and evening.

Although according to the temperature regulators, no heating was active, with open windows we had 22-23 degrees, which means the underfloor heating was still active, even though we hadn’t set it.

Without knowing all the settings of the entire heating system, there are many possible reasons for this. Was the sun maybe shining?

Unfortunately, no one explained that to us. However, the analog regulators also show temperature numbers. We also had that in the apartment.

Yes, unfortunately it is often the case that too little is explained. The temperature numbers on the analog regulators are purely decorative and probably mean nothing.

Underfloor heating systems are much too sluggish due to the thermal mass aka heated screed to be sensibly controlled with individual room controllers. This might work better with very high supply temperatures and poor insulation than with new buildings and heat pumps. E

No, but first, not by more than 2-3 degrees difference, second, always only with efficiency loss, because the neighboring rooms that have a higher desired temperature heat the other room as well.
Secondly, with an efficient system, you don’t adjust the desired temperature every day on a (poor) controller, but set the heating to the desired temperature from the start. This includes, on the one hand, determining the volume flow and the laying distance based on a predefined flow temperature, which should be kept as low as possible.

That means I have a bedroom that is always warm which I don’t want...

Your construction company or the heating installer just gave you bad advice or did the bare minimum.

Definitely!

Nothing, but they are legally required and an exemption seems complicated and unlikely, although possible (according to experience reports here in the forum).
Ultimately, the recommendation here is either to ignore the ERR (individual room control) (constant maximum setting) or even deactivate it by unscrewing the actuators at the heating circuit distributor or switching them off from power (only when powered off: open).

Sorry for the stupid question, but how and where do I switch off the power then?

Something like that. District heating water arrives at the heat station in the house at 70-90°C. That means the flow temperature at your heating circuit distributor is still at least 60°C. With that you get the floor really warm and at full output it’s actually already too warm.
At the moment, for example, I have controllers in my condominium that display 5 stages but actually only know on and off. That means when I turn it up, during the transitional season it actually gets way too warm and I adjust it several times a day or simply only have full heat in the bathrooms and in the other rooms really only when needed.
Since the heating water is already that hot, efficiency isn’t high anyway and the loss is thus limited.

We probably should have decided on district heating.

Without knowing all the settings of the entire heating system, there are many possible reasons. Was the sun shining perhaps?

Which settings or values would be important to be able to give a proper assessment?

That means I have a bedroom that is always warm, which I don't want...

Not necessarily. Of course, you can turn down the volume flow for the bedroom at the radiator valve until you reach your desired temperature.

Sorry for the stupid question, but how and where do I switch off the power?

Not stupid at all, because there is no switch for that. You actually have to disconnect the cables from the motors. Not everyone just does that.
Step one should be going to the heating engineer. He should perform a hydraulic balancing if it has not been done already. Then you can search here or generally on the internet for "thermal balancing." This is a topic for several days if not weeks, since underfloor heating, as already wrote above, reacts very sluggishly.

We probably should have opted for district heating.

I don’t think so. District heating has a clear advantage, and that is the space savings in the connection room.
Disadvantages are: dependence on a monopolistic supplier, namely:
- financially
- technically
as well as higher consumption costs and an inefficient heating system.

Which settings or values would be important to be able to give a reasonable assessment?

See above "thermal balancing."
Otherwise, you need people who are more than just well-read laymen.
Maybe will check in here again, he knows quite a bit.