Yes, the system has to be paid for + the monthly fee.
On paper, it all looks quite nice, but I don't trust these promises at all. That's why I turned to the forum because I have absolutely no experience in this regard and in my region almost everyone who builds new relies on the combination of gas + solar thermal because "…this new stuff is useless anyway…" and so on.
So, it's best to buy a photovoltaic system + storage and cover the heat pump and your own consumption with it and get some money back at the end of the year from the feed-in tariff? However, I have to pay taxes on that, correct?