Hydrogeological Report - Geothermal Energy, Air-Water Heat Pump or Ice Storage?

As already mentioned, the most important thing is the roof. It's best to think about photovoltaics right away, so you don't have to climb up twice. Then, do the basement ceiling yourself, then at least "look at" the windows and doors. External insulation should always be the last step, as cost/benefit is often not favorable.

We would prefer not to clad the exterior facade (brick) with an ETICS. What measures can you recommend?

What is between the brick and the interior wall? If it is just air, you can still gain a lot with blown-in insulation. If there is already mineral wool in there, focus on the windows and the attic.

The current energy consumption (gas) is about 25,000 kWh per year. The living area is about 125 m². The house is detached. Temperatures in winter are max. -10 to -15 °C.

I am feeling dizzy from the numbers. Why 25,000 kWh? My house is bigger, older, and (significantly) worse insulated and currently costs the equivalent of 3000 liters of oil. Is gas currently more than twice as expensive as oil or is the house "leaky"?

My house is larger, older and (significantly) less insulated and currently costs the equivalent of 3000 liters of oil.

That is currently just under €4,500 heating costs or 30,000 kWh. Not much more than the OP. But oil is currently a bargain compared to gas. Still a disaster...

As already written, the most important thing is the roof. It's best to think of photovoltaic panels right away, so you don't have to go up twice. Then, do the basement ceiling yourself, then at least "check" the windows and doors. Exterior insulation should always be the last step, as cost/benefit is often not favorable.

That sounds like a plan. I have another question: What do you think about milling in underfloor heating into the screed instead of doing everything anew? It is supposed to be cheaper and much faster because the screed doesn't have to be removed and dried. As a disadvantage, I have read that the heat is not distributed and stored as well in the floor, meaning there are also cold spots on the floor. Due to the lack of practical examples, I haven't been able to get an impression anywhere yet. Maybe someone of you has had experience.

What do you think about milling a floor heating system into the screed instead of doing everything new? It’s supposed to be cheaper and much faster since the screed doesn’t have to be removed and dry.

Nothing. - inflexible in terms of installation distances - usually only thin tubes - not much cheaper than doing it "properly" - disposal and new screed are subsidized (as long as the subsidy for the new heating system is claimed)