I won’t say anything about the stove - you yourself say that the main argument is coziness. If this factor is very important to someone, they should also spend the money on it without feeling guilty.
Solar thermal energy - in combination with the air-to-water heat pump, I would rather consider photovoltaic in your place. You partly use the electricity produced yourself. Possibly you also run the electricity consumption of your air-to-water heat pump through it. Thus, not only is the ideological approach fulfilled, but it is also (partly) economically reasonable.
We have a 175 l tank with our Vaillant pump (geothermal). 4 people. Last weekend, for the first time (in over a year), we noticed that it was not enough (after bathing 2 children, 1 extensive shower, my wife could no longer fill the tub to the brim with warm water). As far as I know, the tank is usually emptied to X% before cold fresh water is added again, which then needs to be heated. It was probably the same for us last weekend.
In addition, the water in the tank is heated to a certain temperature. When drawing water, cold water is mixed in to reach the comfort temperature. Thus, from 175 l of hot water, XXX l of water with comfort temperature is produced.
If I just wrote nonsense - please correct me.