Heat pump or solar thermal with radiators

Hello, I am not sure if I am in the right place here, but I'll give it a try:

We have fallen in love with a house, everything fits so far except for one thing. The heating/hot water runs entirely on gas ([Gasdurchlauferhitzer]).

The house was built in 1886 and was completely renovated in 2001 according to the [Gebäudeenergiegesetz] (the heating system is about as old). Here are a few points:
- Radiators are installed only in the bathroom and partly in the living room with underfloor heating
- no basement
- very small utility room approx. 4 sqm approx. 1.14 m wide and 4.08 m long
- low ceiling height (downstairs approx. 2.15 m and upstairs 1.96-1.98)

Now we are of course considering what could be done alternatively and therefore my questions here (see it as a kind of brainstorming for idea generation):
- Energy consultant suggests solar thermal, but the storage tank probably won’t find space in the utility room?
- Would an air heat pump be possible only with radiators?
- What other solutions are there? There is no chimney either. Since I don’t have much experience, I am a bit stuck.

I hope the data is useful, it’s just about a few ideas and not a finished solution.
Thanks!!

- Energy consultant suggests solar thermal, but the storage tank probably won’t find space in the utility room?

And which heating system does the consultant suggest? Solar thermal provides hot water in summer – in winter without sun not much happens.

- would an air heat pump only work with radiators?

That can work on the property. You have to calculate the heat load of the individual rooms and which radiators (in connection with a heat pump) are suitable for this.

- what other solutions are there? There is no fireplace either. Since I don't have much experience, I’m a bit stuck.

I would see if I could get a heat pump.

You don't want to live with the ceiling heights - do you? Is there any room for adjustment in the ceilings or does the structure not allow that? That would be a deal-breaker for me ...

You don’t want to live with those ceiling heights, do you? Is there still some leeway in the ceilings or does the construction not allow that? That would be a deal breaker for me ...

I thought so too. 1.98m. How is that supposed to work? But it has the advantage that you have to heat less 8-)

Hello, I'm not sure if I'm in the right place here, but I'll give it a try: We fell in love with a house, everything fits so far except for one thing. ...

It's like love for a woman ;) At first, you see everything through rose-colored glasses. But a building renovated 20 years ago according to the Building Energy Act, where the too low ceiling heights (not living space according to DIN!) were not raised ... that was money thrown away, right? Who does such nonsense? I would never in my life invest in such a building, and I myself still have a building in the family since the beginning (around 1750) with partly very low ceiling heights. When that's gone at the end of the year, I'll be relieved. Never ever would I choose something like that to live in if I couldn't raise the rooms with reasonable effort ... Maybe a few pictures say more than words and the house has such an irresistible charm that even I couldn't resist?

Is there still some leeway in the ceilings or does the structure not allow that? That would be a deal-breaker for me ...

Well... one could also call it cozy ;)