Install photovoltaic system with air-to-water heat pump?

Install adequately sized empty conduits (or have them installed). There is plenty to read about this here as well. Please be so kind and use the (unfortunately poor) search function. Not everything has to be gone over three times.

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Roof full, can only be the answer if money is no object,...or it’s not about building technology. The same applies for 100% self-sufficiency, as power to gas solutions currently cost around 100K€.

Roof full is the only correct answer. Ecologically and economically, everything else would be nonsense. In case of doubt, you can look it up at the [Umweltbundesamt], [Fraunhofer Institut], and many other sources that unfortunately cannot be named here.

The subsidy is called "Einspeisevergütung". Currently, depending on the size of the system, it is about a 70% subsidy. Until about a year ago, it was still 100%. That is already crazy compared to EVERYTHING else. But yes. I also hope it goes up again.

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keep dreaming, just because instead of 30m² maybe 60m² is installed, self-consumption does not change.
That means with the same self-consumption benefit and ever higher system costs, the share of own usage decreases.
The 70% only applies in relation to the efficient size of the system.

What is politically desired by the citizen is clear and thus also the motivation.
In fact, only a power mix still reaches the socket, and heat pumps were not profitable for nothing only after the last Energy Saving Ordinance.
At least in theory, if you have to apply 0 as the primary energy factor. :)

The feed-in tariff is anyway for the poPo,...and not a subsidy but so that you have anything at all for the min. 70% loss.

And if you engage with the topic, you will know who Andreas Schmitz is. No one can get more out than with DIY and scientifically researched.

I don’t dream, I have the home ;-) 50% self-sufficiency without storage. Just under 30 kWp. The system will be paid off after about 9 years if the electricity price does not increase. And Schmitz has already expanded once, and I bet there will be more when he realizes how great it would be to run his air conditioners with more of his own electricity. What is certainly true: DIY pays off great. Whoever can, should do it!

One thing has nothing to do with the other. I've watched countless videos of Schmitz and never seen any "mistakes." But also no instance where he explicitly says to only put a small system on the roof. Especially not after installing his split air conditioning units ;)