Construction costs are currently skyrocketing

Wiesbaden (dts News Agency) - In August 2022, the construction of 28,180 apartments was approved in Germany. This was 9.4 percent or 2,934 building permits fewer than in August 2021, the Federal Statistical Office (Destatis) announced on Tuesday.

From January to August 2022, a total of 244,605 building permits for apartments were granted - this was 3.0 percent or 7,624 fewer than in the previous year period (January to August 2021: 252,229). The results include both building permits for apartments in new buildings as well as for new apartments in existing buildings. In newly constructed residential buildings, a total of 211,636 apartments were approved from January to August 2022.

This was 3.0 percent or 6,622 apartments fewer than in the previous year period. The number of building permits for single-family houses decreased by 15.8 percent (-10,374) to 55,260. However, a base effect due to the expiration of the [Baukindergeld] in the previous year must be taken into account, according to the statisticians.

Accordingly, families with children could apply for the government subsidy if they had a building permit for owner-occupied residential property by the end of March 2021. The [Baukindergeld] contributed to the fact that almost 7,400 more single-family houses were approved in the period from January to March 2021 alone than in the first three months of 2022. For two-family houses, the number of approved apartments from January to August 2022 decreased by 2.8 percent (-612) to 21,176 apartments.

I have to be honest, I can't really imagine how someone builds on 300sqm detached. The only thing left is basically the buffer strip, right?

Yes, pretty much. But the surroundings are worth a lot (central location, parents next door, etc.). So the kids, for example, have the swing in the parents' garden :-)

The heating load is not about the annual consumption, but about the value of heating energy you need at the design temperature. I don't know that now, but based on your other data and unless you live at the North Pole, the unit is obviously much too big. Your heating load will certainly be below 6 kW, maybe even significantly lower.
The problem is less that it has too much power "on top" (so the 12) but that it cannot modulate down. In other words, you only need the 6 kW from my example when it's been -12 degrees for three days. For the other 98% of the year, you would get by with 2-3 kW. Yours can't do that, which is why it will turn on and off more often.
Presumably, that's why the installer put a nice large buffer tank in for you.
But if the damage is already done, of course that's annoying.

Thank you for your explanations, that certainly makes me think.

I have to add that the buffer tank has a modulating electric heater and the plan is that the photovoltaic system will mainly take over the heating function in the transitional period/summer, so that the heat pump won't turn on and off so often. But that would actually argue for sizing the heat pump differently. Hmm, damn it, but that's just how it is now :-/

A quote for the photovoltaic system just came in:

9.72kWp
3 roof sides occupied
405W modules
No storage
No wallbox

Exactly 20k gross including installation without scaffolding.

Really intense offer. 20K gross = net because it would probably only be installed in 2023? You would have 24 modules and that on 3 pages? Does that make sense?

3 roof sides with or without shadow management? Anything special about the inverter? Sounds "expensive" to me at first, but maybe already the new standard?