air heat pump in combination with solar, optional gas connection

This is really nonsense now. A properly planned heat pump also provides efficient heating or hot water even in our German winter.

It makes sense to combine such a system with photovoltaics, as you can sell the surplus and use the generated electricity for hot water, ventilation system, TV, or other household electricity.

Photovoltaics + air-to-water heat pump is a good combo - we have that.

But you have to actively manage self-consumption. On 15.2. we produced 18 kW but only used 12 of it. Weekday, after all.

On 16.2. we also made 18, but used all 18 ourselves. First shower at noon, laundry and dryer running, left dishwasher running... Saturday, after all.

We have a 5.4 kWp system with direct south orientation, 2/3 south, 1/3 west. 22 degree roof, no shading, near Berlin. And 8 kW storage.

Right now today we've already fed in 7.2 kW, there's 1.7 coming from the roof and the storage is full, and no one home who could use the electricity.

Perhaps the OP should first explain what he means by "luftwärmepumpe" and what he means by "Solar-Anlage"...

As already mentioned above. There is no x and y. There is only an x xor y.

If a gas connection exists at all, it will cost you around 4-5k€ without the gas heating, plus the gas heating itself.

For the heat pump, you don't need a gas line; however, the air-to-water heat pump is simply more expensive. As I once read, both options are equally expensive after 20 years. They are just different concepts. Photovoltaics are a good support over the whole year. But they hardly bring anything for the air-to-water heat pump in the months Nov-Feb. Which is not a problem! The photovoltaic system is primarily not meant to operate the air-to-water heat pump in winter.

My combo is air-to-water heat pump + photovoltaic + fireplace. That's what I will probably feel comfortable with starting next winter. If the air-to-water heat pump fails, there's still the fireplace. Then I can wait for a service technician for 2 weeks in winter if the air-to-water heat pump breaks down :p

The additional cost is economically roughly the same. However, with poor planning, the heat pump quickly becomes more expensive than the gas heating.

Regarding the development of future gas and electricity prices, I would probably bet on electricity, but this only becomes really noticeably relevant with the second heating system.

Since you are already thinking about the technology, I would continue to inform myself and decide based on sympathy.

The following makes sense: a) gas + solar thermal or b) heat pump without anything else (monovalent).

The heat pump and heating surfaces must be well planned (google typical mistakes). If you cannot arrange this with your provider, I would choose gas. Otherwise, the heat pump would be my favorite.

For comfort reasons, I would personally always choose a ventilation system. Gas + controlled residential ventilation instead of gas + solar thermal is possible depending on the provider.

I would always put photovoltaics on the roof regardless of the heating system. With a heat pump, photovoltaics pay off a little faster.

The line of thought is not bad, gas + solar thermal or heat pump monovalent.

And search for sources of errors... do you have typical keywords I can use to find more targeted information?

How complex and expensive is a photovoltaic system? Would a reconstruction be unrealistic and not well thought out due to the already installed technology?

The combination of air-water heat pump + photovoltaic + fireplace also sounds interesting....

Thank you.