Decommissioning gas heating: What alternative heating systems?

I also advocate for an exchange against a used gas heating system. Then set the rest to [Wärmepumpe ready]. Improve insulation spotwise, seal windows if necessary, insulate the roller shutter box, etc. Then lower the flow temperature as much as possible, perform thermal balancing.

For a house with nearly 150 kWh/m²/a consumption, you will have to do a lot more than just insulate "spot-wise."
Especially since I understood it as either insulating the entire envelope of the house or not at all. If you insulate spot-wise, you create thermal bridges; the walls will inevitably turn black somewhere and start to smell funny.

What is your flow temperature?
Not that the underfloor heating is designed for 50-55°C.
Then it becomes doubly difficult with the heat pump...

Maybe you’d rather look for a brand new gas heating system, put solar thermal on the roof, turn the heating down by 2°C, and hope the boiler lasts another 27 years?

In a house with nearly 150 kWh/m²/a consumption, you will have to do a lot more than just insulate "spotwise." Especially since I understood it as either insulating the entire envelope of the house or not at all. If you insulate spotwise, you create thermal bridges, the walls will inevitably get black somewhere and smell funny. What is your flow temperature? Not that the underfloor heating is designed for 50-55°C. Then it gets doubly difficult with the heat pump... Maybe you'd rather look for a brand-new gas heating system, put solar thermal on the roof, turn down the heating by 2°C and hope that the boiler lasts another 27 years?

No idea what you understand by spotwise. Certainly not just sticking an insulation board on the facade and done. Spotwise means for me in this context that the areas with the greatest losses are addressed. Drafty windows, upper floor ceiling, basement ceiling, all these are measures with low investment and great benefit.

I understand "punktuell" exactly as "punktuell" means. Doing insulation here and there, but not improving or fully insulating the entire thermal envelope of the house. Otherwise, we would have to discuss the exact, precise wording and the consequences if it is not done.

If a layperson implements your suggestion and approaches a company with the idea that they want to "insulate punktuell, where it has the greatest benefit," then only

eine dämmplatte auf die Fassade kleben und fertig

can come out of it.

I understand "spotwise" exactly as it means. Doing insulation here and there, but not improving or fully insulating the entire thermal envelope of the house. Otherwise, we would have to discuss exact, precise wording and the consequences if one does not do so.

If a layman implements your suggestion and approaches a company with the idea that he wants to "insulate spotwise, where it has the greatest benefit," then only this

can come out of it.

But that presupposes that the company knows as much as the layman. The company will surely explain to the layman that they will not just "stick an insulation board in the middle of the house wall" to achieve the desired effect. At least as a layman, that is what I am currently used to from the trades at my construction site.

There is a lot of room between complete and no insulation at all. It starts with airtight windows and roller shutter boxes, goes over a (in EL) 1500€ expensive basement ceiling insulation, up to the insulation of heating pipes in the basement.
Facade insulation is a very expensive option that only pays off over the years.
By the way, you can also insulate pointwise in the literal sense. For example, with wedge insulation on cantilevered balconies.
Finally, it is common to ask for clarification on certain words to avoid talking past each other. Unfortunately, this is something you do not want.