I can confirm what has been written so far. That is what I was told as well.
At first, I also thought "that sounds wonderful, supporting the heating, especially in winter when you light your fireplace more often. But the cost-effort/cleaning is clearly not cost-effective."
What should also be considered when choosing the fireplace is that it is not too strong (especially in modern / well-insulated houses with underfloor heating, etc.). But as has been written here several times, every element (heat pump and also the stove) should be well matched to the (energy) needs of the house.