Central room temperature controller for ERR underfloor heating

It is always a matter of setting
And when everything is perfectly coordinated, then the room thermostat can also make sense. And that even though it is actually only a temperature limiter.
I just wanted to say that you should not imagine the heat pump pushing against the closed valves with swollen hot cheeks while the full volume flow runs through the open valves. It automatically detects the demand through the requirements and regulates itself. This allows a bit of energy to be saved.

If your heat pump provides too high supply temperatures, then the heating curve is set incorrectly.

One should read up on hydraulic balancing and the self-regulating effect.

ERR might make sense in rarely used rooms with possibly changing usage types. (Hobby rooms or something like that).

If the balancing has been done properly and the design of the underfloor heating (this is a prerequisite, otherwise it becomes difficult) was done correctly, then the ERR does not have to regulate anything.

Through the balancing I regulate that the individual rooms receive the necessary flow according to their requirements (room-specific heating load calculation). The heating system only provides one supply temperature. Not a different one for each room. In contrast, an ERR opens or closes.

Can this ERR/heat pump discussion actually be applied to modern gas heating systems with solar support?

The self-regulating effect is amplified by an ERR, which also speaks in favor of thermostats.

Here is an example of what a thermostat can be good for:
Here, the outside temperature has been consistently 15-16°C for a week, sometimes even colder at night. The heat pump is set so that warm water for the underfloor heating is only provided from 18°C outdoor temperature onwards.
However, since it was so warm for weeks before that the masonry heated up and this heat emission still keeps the rooms at 22°C, the thermostats shut the valves.
Therefore, I have no heating demand and the heat pump only heats for the storage.
Of course, the energy for heating the warm water for the underfloor heating would be relatively low due to the heating curve, but the pump would still run continuously and consume electricity. Pumps, efficient as they are, consume relatively a lot of power during operation and are one of the highest wear parts in the system.

It's always a matter of settings
And when everything is perfectly coordinated, then the room thermostat can also make sense.

And if that's the case... you don't need an ERR.

To take another example.

You have 10 rooms. 2 of them currently need 30 degrees supply temperature. But these are the bathrooms, so relatively little volume. All others need less. The heat pump doesn’t differentiate, so you have it set to 30 degrees supply temperature currently. What happens? In 8 rooms the ERR closes. In two it stays open. The heat pump sends out 30 degrees and has a minimum flow rate. It wants/has to get rid of the energy. But it doesn’t because the ERR closed 8 rooms. So what happens?
Depends on the system.
Either you have a heating buffer in between, so the heat pump stores the energy in the buffer. Bad because until it is needed again -> energy loss.
Another or additional way is the bypass valve, so the supply is sent straight back into the return and circulates.

This is a bit exaggerated but is meant to show why ERR usually does not contribute to energy saving.

Well, without ERR no heat would be transferred to the underfloor heating and the high return temperature would cause the heat pump to shut down, avoiding the expensive pointless heating of the storage tank. Maybe you can also lower the heating limit, 18°C for a new building is already high, I think.