What to replace an oil heater from 1989 with in an old witch's house?

If I remember correctly, you only have to replace the heating system when the owner changes, and then immediately. Otherwise, old oil burners have grandfathering protection.

I also don't know if a heat pump is worth it without photovoltaics.

The longer I deal with the topic, the less convinced I am that photovoltaics contribute much to the heat pump. In winter, the days are short and mostly gray anyway, so not much photovoltaic electricity is generated. And when the sun does shine (at least in new buildings with many floor-to-ceiling windows), you usually gain enough heat from solar gains. Additionally, the wiring seems to be somewhat more complicated if you want photovoltaic electricity for general power and a heat pump behind a separate meter.

Does liquefied gas from the tank have any advantages over a pipeline?

The main advantage is probably that you don’t need a pipeline where it would be prohibitively expensive. There are also many people who are much more than 60m away from the gas network. Possibly, you can also save a few euros compared to a continuous tariff by buying at a favorable time, but that is probably a minor point.
And regarding power outages... how often does that happen? I can do without heating for 5 minutes a year. Even a longer power outage in this country is at most half an hour. Not half a week like in America ;)

Ha, great. I had exactly this one in my house....and after the sale, it still runs.

Hmm, from my understanding, with a heat pump you always still have an electric heater as a fallback, since it comes with a heating element?

That is often the problem. Read here and you will see that you have to deal with it and it is not a no-brainer. The installers often don't know their way around and repairs are very expensive.

Does liquid gas from the tank have any advantages over a pipeline?

The tank is located right at the house or is buried. You can buy it or rent it....It's all a matter of calculation. Depending on the situation, at least it is something to think about once.

Ha, great. I actually had exactly that in my house....and even after selling, it still runs.

That is often the problem. Just read here and you will see that you have to deal with it, and it’s not a walk in the park. The installers often don’t know much about it and repairs are very expensive.

The tank is located directly at the house or is buried. You can buy or rent it....It’s all a matter of calculation. Depending on the situation, you can at least think about it once.

So the tank has virtually no advantages over the pipeline. If you rent, you are tied to the provider you rent from. They can charge any price for filling.
If you buy, you have the obligation to have it inspected. Every 10 years, I think. Whether it is cheaper than having 60m of pipe installed... no idea.
As a fallback solution, only an independent chimney without water connection would be possible.

Hmm after a lot of research my current favorite is a Panasonic split heat pump. Hot water generation via a hygiene buffer tank with a downstream instantaneous water heater for hot water production. Our water is quite hard (21H), I don’t know if I need a descaling system?

In addition, another stove. I haven’t seen it live yet, but we like the design. Since the stove, unlike a water-based one, doesn’t require electricity, even during a longer power outage (which hasn’t happened in the last 30 years anyway) we won’t be left in the cold. In my opinion, a water-based wood stove entails a huge amount of complexity, my motto is rather KISS (keep it simple stupid).

Depending on calculations and subsidies, I would then put a solar system on the roof. The question is whether only on the SW or also on the NE side. Later, when electricity storage becomes cheaper, I might retrofit some, but at the moment no technology really seems convincing. Saltwater batteries still seem underdeveloped, and I find lithium problematic not only for environmental reasons. In the transitional period I could probably store solar surpluses in the hygiene tank of the heat pump and thus maybe heat a little less at night.

To make the heat pump work well, I would possibly upgrade some radiators (the existing ones are over 30 years old and in some cases there is room for bigger ones) and partially switch to better insulated windows. Soon I have a few appointments with heating contractors to get offers, let’s see what they say. For me it would be okay to pay 10% more per year if I get a cool stove in the living room + no stress with gas deliveries or a pipeline.

It’s still not clear to me what to make of the heat pump electricity tariffs. With the hygiene buffer as a buffer it might work, but I have concerns that the shutdowns will come exactly at the peak loads on the grid, i.e. at midday, when pumping would be particularly attractive.

Currently there is a 45% subsidy + possibly a small bonus from the district. What do you think how this will develop in the next few years? I don’t have any urgent pressure to act at the moment, but the heating could fail at any time and inflation might also speak in favor of acting on this rather than the coming summers?

Well, then now in the next warm period upgrade the house accordingly. HK as large as possible, carry out energy renovations. That benefits every heating system. Next winter test how low you can go with the VLT. And then decide which system makes sense.

Domestic hot water generation via a hygiene storage tank with a downstream instantaneous water heater for hot water generation.

Why use an instantaneous water heater? The Panasonic can usually operate down to -15 degrees without an electric heating element. So just add an electric heating element as a supplement in the hygiene storage tank so that it is only switched on when really necessary (controlled by the heat pump).

I am still unclear about what to make of the heat pump electricity tariffs.

Usually nothing.