Air-water heat pump current consumption and data

BDT was 0.7 for me. According to the energy consultant, a good decent value.

Good value we were at 0.9 nevertheless that says nothing about thermal bridges.

I wouldn't overdramatize this now even for the transition period. However, you did have disproportionately high heating costs in the winter. So no matter what, you will have to do something, whether it means continuing to have/pay higher electricity costs.

If I were you, I would first get the family used to "normal" room temperatures so that you can turn down the return flow.

I know you have already tried that. But you have also given in yourself.

Yes. An uninsulated house is just as "good" as your insulated house. So the problem with you is not the heat pump, but the house itself.
Who knows how "good" your house actually is and not just nicely calculated on paper.

On paper, every average would be "nicely calculated" compared to another wind location.
Hardly any house behaves like the average.

Actually, right now is the perfect weather for air-to-water heat pump + solar + battery: AT > 6*C, so no energy-consuming defrost cycles, heat pump regularly almost empties the battery for heating purposes (we have felt max. 13 *C AT here for weeks), ...

It would be more sensible to let the screed be overheated by one or two degrees directly by the sun during the day. Then the heating does not need the expensive battery power, the heat pump runs more efficiently during the day and you are less likely to hit the 70% throttling. All in all, money saved and something done for the environment.

Hardly any house behaves like the average.

No, but a house with a heat pump is energetically better on paper than one with gas or even oil. And that with otherwise completely the same construction method and location.
Once KFW 55 is indicated, once efficiency house, and with oil it would not be buildable.