Heat pump is not compatible with a water-bearing fireplace

What exactly is your problem? So is there a real problem, or simply that you can't imagine that many tons of screed can't cool down such a small storage tank quickly? How is the heating circuit connected? Is there a mixer and its own pump available?

Yes, we probably can't imagine it.
Because if I have 75 degrees and in the underfloor heating there is always only a loss of 5 degrees, it only has to compensate that, right?

I am a layman and will try to explain. Please don’t take it too seriously. I don’t know much about heat pumps.

You have a buffer tank with a heating element, a supply and return line for the fireplace, a supply and return line for the heat pump.

You draw your hot water from part of the buffer tank. The hot water should be at least 55, preferably 65 degrees Celsius.
When do you heat the fireplace? Surely not at 20 degrees outside temperature. What if there is no sun today and the photovoltaic yield is almost zero.

Exactly. We have it set to 55 degrees but would like the hot water to be even higher. Which, as mentioned, also works wonderfully as long as the underfloor heating is off. At 20 degrees, I don’t stoke the fire, but at slightly less, I do, in order to save electricity… that’s the idea.

Theoretically, everything sounds good. I would have installed the hot water generation and the heat pump separately. Technically, your hot water generation works as an instantaneous water heater. So today your hot water is generated electrically. I assume that the heat pump tries to generate the hot water as well.
The heat pump does make the hot water with heat, yes. That’s why it runs constantly and consumes a lot of electricity.

I think there are problems with the control, priority switching, etc.

Your buffer tank consists of 3 parts: the heating water tank, the solar heat exchanger, and the domestic hot water heat exchanger.
It is surprising that your domestic hot water heat exchanger has a volume of only 56 liters. The solar heat exchanger only has a capacity of 17 liters. There should be 2 heating elements installed with 9 kW each. So if your hot water is heated flow-through, the electricity meter runs at 18 kW. You probably have a cheap electricity provider. Or you shower little.

The 56 liters also surprised me, but it would be much according to

The fireplace is only meant to add heat to the heating circuit. The heat pump supply will always keep the water at 35 degrees supply temperature. And you have 250 square meters of living space. The water will cool down by more than just 5 degrees. If I heat with 50 degrees supply, about 20 degrees return to the oil heating. The heat in the house has to come from somewhere and underfloor heating is only a large heat exchanger.

As it stands, it runs in at 35 degrees and returns at 32-30 degrees. I don’t understand that, because as you say it must heat a lot. I am also someone who likes it warm, 23 degrees in the living room and warmer in the bathroom.

At least you were clever enough to have a fireplace installed. Many don’t have one. When I come home freezing from skiing in winter, I want to sit by a warm fireplace or at least a hot radiator, not in a minimally tempered house. One gets old too. I am old enough and can very well decide for myself how to heat. I don’t need green moral apostles who say you can fly somewhere for 50 euros but I should save the world’s climate with my heating. No thanks.