Construction costs are currently skyrocketing

For that, the CO2 is marginal. ;) You have to die somehow; energy from nothing does not exist. Electrically powered heating systems like heat pumps rely on coal and gas in the background, French nuclear power, hydropower from sustainably flooded Alpine valleys, or wind power from spoiled landscapes, likewise ground-mounted photovoltaics are not a sight for sore eyes. We don’t even need to talk about all the nonsense happening in the supply chains, we wouldn’t finish today otherwise. The same goes, of course, for the house where the heating system is located, because truly environmentally friendly construction is not possible. The world is simply not a glossy brochure.

But fine dust is also generated here, but compared to wood burning it is marginal. See graphic.

Yes, crazy. Now I am a bit shocked by the rather poor values of a heat pump (and the comparatively good values of a pellet heating system). Presumably this is considered without photovoltaics? The wood stove is actually quite good in terms of CO2, but unfortunately a negative frontrunner in terms of dust.

Look at the graphic at the bottom right.
A rogue is who thinks badly of it.

Although the environmental agency currently really sees burning wood as CO2 neutral.
Although that is simply not the case in such quantities.

Look at the bottom right of the graphic.
A scoundrel is who thinks badly of it.

Although the environmental agency currently really sees burning wood as CO2 neutral.
Although in these quantities, that simply is not the case.

Ah yes, I didn’t even look there. How does it go? Trust no statistic you haven’t manipulated yourself (although I don’t want to imply anything here, since I haven’t dealt with the matter and therefore don’t want to allow myself an opinion).

Hard coal is somewhere around 800-900, lignite around 1200g CO2 per kWh. I don't know the fine dust values, but in the industrial sector it is often better than in private fireplaces. Appropriate saying at this point: Trust only the statistics you have falsified yourself :D For BEVs, the CO2 footprint (car + battery) is often given using [DrittelMix Stroim], likewise for heat pumps. However, if both are powered entirely by renewable energies, the "footprint" for the BEV drops to only about 2g CO2 per km (compared to about 40-50! with [DrittelMix Strom]). I don't know any values for heat pumps, but it should also result in drastically better values.

Well, it doesn't look that different at the Federal Environment Agency either.