This may be where it s stemming from in your yard as you mention that the fungus seems to be limited to growing on the siding closest to your mulch beds.
Brown stains on house siding.
That might have been part of the problem.
Brown stains on house tips.
Given that this one had mushrooms growing out from between the siding planks i told them to remove the siding in this area.
Brown stains on side of house tips below.
Brown syrup like stains streaking down the siding on the exterior wall of the bathroom.
Weather conditions before stain appeared are critical.
Stains originate just above metal z flashing.
Otherwise the situation is exactly like what i see on 50s houses.
Black brown or gray stains on roofing products due to debris left on the roof surface such as piles of leaves and.
Artillery fungus is difficult to get rid of because of its sticky properties.
Black or other colored stains on roof surfaces may be caused by soot from chimneys both wood fired and oil fired.
Cedar has natural preservative chemicals that dissolve in water.
No clue about the rest of the house.
I have often seen red or brown stains from water leaking down behind building siding on older homes.