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

I am currently also reading about water heat pumps. That would free up the chimney for the wood stove in the living room.
We have a creek that flows through our property, about 20-30m away from the house. That’s why I suspect that you wouldn’t have to drill too far to reach the groundwater. I think the creek doesn’t carry enough water to take the heat directly from the creek, or the distance is too great. Next to the house there is an approx. 2 x 2.5m waterfall on public land to which the municipality now wants to add a fish ladder.

Not that you confuse the terminology. You probably mean a heat pump where you extract the energy from the groundwater?? That is something entirely different from a domestic hot water heat pump. This one takes its energy from the ambient air. You have to look closely into the groundwater and creek usage. There are strict regulations concerning such usage.
I think you have to become clear about the basics or what exactly you want to renovate. In any case, there are various options.

Yes, by water heat pump I meant a heat pump that draws energy from the groundwater. Yes, water rights at the stream are a complex matter. But I think using groundwater would be more interesting anyway.

Basically, I find heat pumps very appealing. With the hopefully saved maintenance costs for the oil heating system, I could probably supplement heating electrically in case of illness or laziness, and the chimneys would be free for a water-bearing fireplace in the living room. This would be located directly above the current heating system, so fresh air supply for the stove could be fairly easily ensured via the basement, and it wouldn't be too difficult to connect it to the existing pipe network (I assume).

What do you think about it?

Oh dear.... :D there are a thousand opinions and most of them have their justification. As a rule, nowadays people install air-to-water heat pumps with underfloor heating; if you do it differently, there are few supporters, because of course everyone usually swears by their own system. But it has always been like that and should not influence the decision alone. So if you are not planning a complete renovation anyway, I would consider replacing the entire heating system. You can read up and down about CO2 and all these discussions and you won’t necessarily get any smarter regarding your own situation. If grandma manages with it, I would leave it as it is or install a really nice wood stove and, if needed, targeted infrared heating, there are great options for that. I would especially base it on what grandma wants. Maybe she definitely doesn’t want wood and is looking forward to a modern heating system. You probably can hardly retrofit water-based underfloor heating anyway, although I don’t personally like it that much. So.... it is and remains an individual matter and, in my opinion, depends on grandma’s preferences. Maybe she doesn’t want such a deep renovation at all, then I would leave it as it is and only expand selectively (wood stove + infrared modules).

Yes, water rights on the stream are a complex matter. But I think groundwater usage would be more interesting anyway.

You probably may not use water from the stream; whether you can carry out a drilling you can usually ask by phone at the lower water authority. That has nothing to do with the above-ground stream.

With the hopefully saved maintenance costs for the oil heating, in case of illness/laziness I could probably heat electrically quite a bit

Well then read up a bit here about heat pumps, problems, costs... oldschool systems (gas + oil) are still, in my opinion, mostly much more maintenance-friendly but at least cheaper, also because every heating engineer can repair them. With your intention, the wish is probably the father of the thought. :D

It is and remains an individual matter and, in my opinion, depends on grandma's preferences.

Thank you very much for the information.
Who gives good and suitable advice? Are these energy consultants with special qualifications?
The topic is so confusing, overwhelming, and baffling; it is incomprehensible to me, who has no idea.

The problem is that a complete renovation is actually not supposed to take place, but only new windows and insulation of the upper floor ceiling. But no new pipes and underfloor heating yet, so everything can stay as it is. Also, no full thermal insulation.
It should simply be comfortable, which is why it was converted to night storage heating back then, and the stoves were thrown out.
However, she would like the kitchen stove because of the little water pan, for cooking plum jam, etc.
That also brings back childhood memories.

The infrared heating sounds good; we had already considered it, so we will keep at it.

Hmm as long as we have the old oil heating system, in my understanding no additional wood stove may be connected to the chimney.

Who advises well and appropriately? Are they energy consultants with special qualifications? The topic is so confusing, unmanageable, and bewildering, it is incomprehensible to me, who has no idea.

You are right. We now live in Saxony, and I found it very difficult here to find an energy consultant who does more than just give standard statements. In the end, it was an energy consultant based in southern Germany; he costs a bit more than the cheapest ones but is worth it! Here, people just shrugged or even dismissed it because of compliance with the Energy Saving Ordinance, and now we are building KfW40Plus with the same basic technology. I got the impression that people only like cookie-cutter solutions that they quickly calculate and call it done. I had good experiences with the consumer advice center here. It was already really helpful on the phone, and then there is a free initial consultation by a proper energy consultant. It’s best if you post your project with questions in a separate thread and see what information you get; otherwise, it will derail ’s thread.