Old gas heater defective -> need a new one, but which one?!?

That already sounds adventurous... without underfloor heating, gas will probably be the only sensible option.

Maybe have someone calculate where the air-to-water heat pump + new low-temperature radiators - subsidy stands. But it's best to get the air-to-water heat pump offered by another company.

I have calculated that we are currently consuming about 110m³ of gas per day

That's a casual 50€ heating cost. Per DAY!!! Besides the problem that the gas is disappearing somewhere.
You better turn off the heating and rent an apartment via AirBnB or elsewhere before your house is full of gas.

Is that a multi-page certificate and from when is it?

There should also be statements about the energy condition and recommended renovations.

[*]Heating (central heating with condensing combination boiler (natural gas E))
[*]Hot water (central hot water supply via solar system (solar energy) + heating system with condensing combination boiler (natural gas E))