Air-to-air vs. air-to-water heat pump KFW55 house - cooling function important

That is clear to me. The question is why no manufacturer offers suitable indoor units for the regular heat pump (heating system) that can cool in winter. There are also multi-split systems for air conditioners, so why not something like that?

Do you mean in summer? I think every manufacturer does not allow indoor units to have different functions. Or rather, we were explicitly informed with our air conditioner that you cannot have heating and cooling running at the same time.

I understand that. The question is why no manufacturer yet offers suitable indoor units for the normal heat pump (heating system) that can cool in winter. There are also multi-split systems for air conditioners, so why not something like that?

Because the heat pump works largely differently:

* In a split air conditioner, the refrigerant is routed through the lines to the indoor unit and "expands" there so that, simply put, the heat exchanger in the indoor unit is cooled (or also absorbs heat – depending on how you want to see it).
* In most heat pumps, this process takes place entirely in the outdoor unit. Only the water-carrying primary circuit is routed into the house. This is then the heated (or cooled) water which is usually then also routed through a buffer tank and possibly a domestic hot water tank.

Therefore, normal "fancoils," i.e., the indoor units mounted on the wall that you know from split air conditioners, are basically ruled out.
Manufacturers would thus have to create a way to somehow connect the outdoor unit directly. I think that just makes everything more expensive and complicated.

Here as an example a Bosch/Junkers outdoor unit