Air heat pump in combination with water-carrying fireplace

It would just be great to integrate this into the heating system as efficiently as possible.

Contrary to popular lay opinion (or the usual sales strategies and tricks), one should definitely avoid this in a modern and energy-efficient house.

A fireplace in a building subject to the Energy Saving Ordinance is one that stands in the room and nothing more. (Of course including the safety devices)

Here the principle applies: less is more...