Soot and dust dispersed around house which I believe is coming from baseboards

Has anyone experienced this, I've been increasingly seeing this very fine black dust on surfaces around my house and every time a surface is wiped down there usually is dust, I just noticed right above the baseboard there were dust marks so now I'm suspecting that's where it's coming from, has anything seen this before and what would be the best way to get rid of it and stop the issue completely?

You need to vacuum your floors more often.

Your picture shows the filth being carried up through your radiators by rising warm air.
Which then is sticking to the wall above.

You don’t say where you are from, but maybe somewhere dusty?

Either way, dust needs to be vacuumed up, Swiffered up, wiped up from counters and tables.

No mystery here.

Maybe something like old carpet padding is breaking down, getting crumbly and dusty.

its a fact dirt and dust is being dragged through that baseboard and being deposited on the wall.... educate yourself.

Maybe you live near an area experiencing dust from wildfires?
Or near enough downwind to get the dust from ash?

If you are in a warm winter area, dust might be blowing in if you are having a drought.

Other fabrics like drapes or carpeting could be breaking down.

Let's put a little more thought into this. The OP does not indicate where he is from, because climate is an important factor, and many posters don't give enough information in their post.
He also notes that he has seen this around the house, but just noticed it above baseboard heaters and questioned if it could be coming from the heaters. My first question would be- is it really dust? My house is dusty. It doesn't take long for dust to settle on horizontal surfaces. I just wiped my hand across a sheetrocked wall and there is NO dust on the wall. Why would dust be attracted to a wall? Moisture could do it, but that would also encourage the growth of mold (typically black mold which can look like dirt or soot) [to differentiate mold, spray a dilute solution of fresh bleach in water on it. If it disappears, it is mold]. A textured wall finish or a fuzzy wall paper might attract dust, but that does not appear to be the case here. IF it were coming from the baseboard heater, I expect that the aluminum fins would be clogged with dust.

I would need more information: climate, location of the dusty areas (only above baseboards? on interior walls as well? only low on walls? Is the rest of the house dusty? Are exterior walls well insulated? Is it really dust?)

Or you could get a rag with some cleaning solution and clean it off the wall. Other than that, I think it's taking it a little too far.

When I see a spider web. Up in the corner of my room. I get a broom and I remove it. I don't go investigating every little crevice in my house to figure out how that spider got in.