Collaboration of air-water heat pump, photovoltaic system, and storage

Hmm okay. But why do these calculations always have to be done "individually" for each house then? So you could also just use the technical data of the respective system to say "System XYZ" produces, for example, 4000kWh of heat from 1000kWh of electricity... Or am I thinking about this wrong?

The BAFA has a calculator for the annual performance factor, which must be used for the subsidy. At least, this was the case before 2020. Individual influencing factors there are the proportion of domestic hot water, the location of the house, and the supply temperature. The latter depends on the design of the heating surfaces and the individual heat load of the house. In practice, the performance factor depends more on the house and the mode of operation than on what is stated in the data sheet. With a buffer tank, poorly planned underfloor heating, and/or a heating curve that is much too high, the annual performance factor can be around 3, with good planning about 4.5.

Or am I thinking wrong right now?

You are thinking quite correctly but not yet all the way through. For the subsidy calculation, this is probably sufficient, but in practice, when choosing the size of the photovoltaic system with or without storage and on which surfaces, a few more questions need to be clarified. The further the feed-in tariff decreases, the more important these considerations become.
Solar power is not available linearly—just as little as the electricity consumption of your household. How much of the self-produced energy you can use for your own consumption and how much you feed in or store is already an important key figure with a factor of 3 between feed-in tariff (registration of the system now) and the electricity purchase price.
You can base the economic dimensioning and equipment of your photovoltaic system on this.
From this forum, I learn that with the heat pump, the optimal consumption values can only be achieved through smart settings and good installation—I don’t know how this compares to the catalog specifications.

Heat pump: The manufacturers only provide the COP for certain conditions, no annual consumption figures. The COP can be used to compare heat pumps with each other. The annual performance factor calculator from Bafa is a good reference for reality, provided the typical errors in installation and operation of the heat pump are avoided.

Regarding photovoltaics, many have clearly demonstrated in other forums that maximum utilization of the roof is generally the most economically sensible option and that, as a rule, you do not save with storage, but rather pay for it.

Bafa has a calculator for the annual performance factor, which must be used for the subsidy. At least that was the case before 2020. Individual influencing factors there are the hot water portion, the location of the house, and the supply temperature. The latter depends on the planning of the heating surfaces and the individual heating load of the house.

In practice, the performance factor depends more on the house and the mode of operation than on what is stated in the data sheet. With a buffer storage tank, poorly planned underfloor heating, and/or a heating curve that is far too high, the annual performance factor can be around 3, with good planning around 4.5.

That is still exactly the case.

And thank you, so the topic is now clarified!

Great information!
Thank you.