Heating load calculation 10.3 kW, is a 9.5 kW air-to-water heat pump sufficient?

The CoP value or the annual performance factor are of course completely irrelevant to the question of whether this heat pump is properly/well sized. Nevertheless, certain values must be achieved (specifically for the location of the planned use) in order to obtain any potential funding.

However, if your heat pump has a nominal output of 8.1 kW at 7 degrees outside temperature and 35 degrees flow temperature, then it will presumably be significantly lower at -12 degrees outside temperature. So if the heating load calculation is correct, it could be a close call once it gets really cold or an expensive one if the electric heater runs then.

The CoP value or the annual performance factor are of course completely irrelevant to the question of whether this heat pump is properly/well sized. Nevertheless, certain values must be achieved (specifically for the location of the planned use) in order to receive possible funding.

However, if your heat pump has a nominal output of 8.1 kW at 7 degrees outside temperature and 35 degrees flow temperature, then it will presumably be significantly lower at minus 12 degrees outside temperature. So if the heat load calculation is correct, it could be a close call once it gets really cold or an expensive situation if the electric heating element runs then.

So the heat pump is too small after all?

How often do you have -12°C? And what is the minimum performance of the heat pump at +7°C and at 0°C?

Is there a website with historical weather data for a postal code? Unfortunately, I couldn't find anything quickly.

Yes, they exist. Search for "Deutscher Wetterdienst" (DWD). There you will find data that partly go back a hundred years and are available in hourly resolution or finer.

You have clearly come across the wrong heating installer here. He calculates the heating load with the rule of thumb area times energy demand + 20% hot water. But that's not how it works.

If you have a heating load of 10 kW for a new build with 252 m2, you built it wrong! Your primary energy demand is also surprisingly high, but still within limits. It should be a maximum of 8 kW.

The heat pump you specified will most likely no longer be eligible for funding in the proposed sizing! The bigger the pump, the worse the annual performance factor. Especially the Viessmann air-water heat pumps stand out negatively here.

A modulating pump should also be as small as possible and not designed for the lowest achievable outdoor temperature. Just because you have -20 degrees twice a year doesn’t mean it makes sense to choose a bigger pump that can handle these 2 days a year. Two days with additional heating rods (which then only run for about 2 hours) are cheaper than continuous operation of an oversized pump. People sometimes talk nonsense here...