heat pump for house !== heat pump for hot water

I don't know what it's like where you're living but here in Switzerland it's completely normal to have one heat pump that does both. Here there's a lot of floor heating, which also uses water, so you usually just run one loop to the "boiler" (a water tank with a copper loop for the water from the heat pump to circulate through) and one through the floor and have a valve to switch which is running through the heat pump.

I have one of these: https://cta.ch/en/private/products/ah-i-eco-innen

I got it in October so most of the time I've had it has been <10C. It's produced 806.3 kWh of heating for hot water and 6587.2 kWh for the floor heating. It consumed 302.7 kWh and 1801.4 kWh respectively, for a COP of 2.66 and 3.66.

Yes, same thing. Heat pump to heat exchanger. This is over 39 years old tech and in common use around Scandinavia and mainland europe. This is ancient technology.

There's a lot of different heating systems: If your heating system uses hot water at any point, (baseboards, hydro-air, underfloor, ect,) using a single heat pump makes a LOT of sense.

Personally, I prefer an air-source heat pump hot water tank. It significantly dehumidifies my basement.

Why not?