air heat pump, water-based fireplace stove, functioning, underfloor heating?

Not at all.

Morning!

That's how it is ;). You can see the wood stove as

- a cozy warmth source and/or
- an emergency heater in case of a power outage and/or
- an additional heater at very low outside temperatures

It will hardly bring any savings, so a water jacket does not necessarily make sense. I would also have (probably unfounded) safety concerns about that.

I would focus on the combustion air supply. Either via a second flue or the outer stone. My neighbors have either a room air-dependent stove (i.e. window tilted open) or air supply through the floor slab (unfortunately it got flooded).

Best regards, TomTom.