Is an air-to-water heat pump sensible for renovation as an efficiency house monument (160% Energy Saving Ordinance)?

If you have Ht and the building volume, you can at least estimate them. Just google Trenchplaner and Ringgrabenkollektor.

Or directly enter grabenkollektor dot waermepumpen-verbrauchsdatenbank dot de/Energieeinsparverordnung-heizlast dot html. The indicated values are surprisingly close to reality and the days-long calculations of HVAC planners.

Then it follows:

Transmission load:	7450	W
+ Ventilation load:	1199	W
+ Domestic hot water load:	400	W
= Total heating load:	9049	W

This is the first step...

Let's see if I understood it. For the consumption calculation ...

(Heating capacity / annual performance factor) * full usage hours * electricity price = electricity costs

9kw / 3 (rather conservative) * 2000 (?) * 0.35€/kWh = 2100€ heating costs. So 175€ / month on average.

Forget the air pump very, very quickly. Step on it, save a lot of money, and have no problems.

Even in new constructions, air-water heat pumps often cause problems due to defects or very high consumption. After a few years, repairs come up, e.g., a new compressor costing 2000 euros, etc.

save a whole lot of money

So first of all, gas is about €20k more expensive than the initial investment (more expensive insulation, no subsidies, gas connection). Operating costs are secondary.
That means "saving" would refer to repairs and lifespan/maintenance. So the air-to-water heat pump would have to be maintained/repaired for around €20k in about 20 years.