Climate Protection Act Schleswig-Holstein

Is a pellet heating system for 25k€ already disproportionate compared to a gas heating system for 6k€, or is it proportionate for climate protection after all?

There is another room between the heating system and the possible storage space. This would require complex conveying technology.

With that, you have already given the answer. It is disproportionate.

A hot water heat pump would not be worthwhile, as my hot water consumption is extremely low.

That would also be disproportionate because you would then need to install new pipes. So far, you only have instantaneous water heaters.

Once again: Just stay relaxed.

But does the additional heat pump provide enough temperature to operate standard radiators?

60 degrees? Is that enough for you?
Otherwise, talk to an energy consultant about switching to a heat pump. Possibly, proper heat pump radiators might already be sufficient for your house. Then add a heating curve 40/34 and it could run efficiently.

Basically, I already use it in the bedroom, with the air conditioner, where I heat up during the transition period.

On the one hand, air-to-air heat pumps (air conditioners) have been (and possibly still are, I'm not fully up to date) subsidized by Bafa if they are purchased "mainly for heating." So I would definitely check that option again.
On the other hand, these things are not so incredibly expensive that it makes sense to install them even without subsidies in some old buildings and use them for heating until it gets down to -5°C or colder. There are also models that operate down to -20°C, but eventually the gas heating will probably be cheaper.

But does the additional heat pump provide enough temperature to operate standard radiators?

Yes. In many cases, a complete switch even works. If the heat output is not sufficient, individual radiators can also be replaced.
It is important to ensure proper flow to the radiators and to keep them fully open at all times. No night setback or similar. This way, the flow temperature can be kept permanently low.
I recently read a study that only noticed significant efficiency losses above 55°C flow temperature (in NAT). 55°C consumes only 13% more electricity than 35°C flow temperature. So you shouldn't get too worked up about it.
Current heat pumps can reach up to 70°C if they use propane as a refrigerant. These models are therefore especially suitable for old buildings and are not immediately at their limit if you need 50°C occasionally.

I would not pursue pellets any further either – the climate doesn't really care whether the CO2 comes from gas or wood. It’s in the air either way.

Otherwise, I would also join and first recommend calmness. Don’t rush anything, plan carefully – there are good possibilities.

55° only needs 13% more electricity than 35° flow temperature.

That should of course have been "13% more electricity".

Thank you for your answers. Well, then I am somewhat relieved and will not worry unnecessarily. But today I have already submitted an application for a gas connection. And hopefully there is a company that can deliver and install a gas heating system in time. I have recently had frequent problems with the shortage of skilled workers.