Buy a house with energy class H and not renovate much?

I think instantaneous water heaters would also be an option for hot water, right? Yes, I have also thought about programmable radiator thermostats to better control the temperature and night setback and so on, especially because of mold.

where the masonry is said to have had an 8 CM air gap into which blow-in insulation was blown in 2017.

Then the facade isn’t actually that bad. Adding more insulation probably isn’t worth it. If you insulate the roof and cellar ceiling with EL, use type 33 radiators, and upgrade the windows a bit, you’ve basically done everything (your parents seem to know their stuff). Go for it. One consideration could be whether you will have the finances to switch to a heat pump in the future (3-15 years down the line), but from the building's perspective, I see little problems. Do it.

Yes well the masonry overall is 42 cm thick, as reserves I plan with 400€ monthly that should be enough for a heat pump in 5-10 years.

Why not? With us (and many that I know) the bedroom window is left slightly open at night. Almost all year round, down to subzero temperatures.

Great for heating costs! May I also show you a few pictures from old buildings of how nice fluff appears in the rooms above the tilted window – of course, the tenant says that the mold definitely isn’t caused by them…
Not to mention cooled down and moldy room corners on the outside.
Unfortunately experienced many times myself.

whereby the masonry is said to have had an 8 CM air layer into which blown-in insulation was injected in 2017.

But that does not fit the energy consumption at all. Have the insulation proven to you, then the house is much more relaxed.

Great for heating costs! May I also show you a few pictures of how nice fluff forms in such rooms above the tilted window in old buildings - of course, the tenant says that the mold definitely isn't caused by him… Not to mention cooled down and moldy exterior corners of the rooms. Unfortunately experienced many times myself.

I never wrote about tilted windows, or where do you read that? Blinds down to about 15/20 cm, then leave one sash slightly open behind the curtain. Heating costs? I like it cool in the bedroom anyway, so the heater is off.