There may be two species of algae here, can't quite tell. But one is definite, and that is the "fur" that is certainly visible on the right branch in the second photo, and it is black brush algae. The other which I cannot say for certain is the odd circular spots on the foreground wood right in front of photo 1, but this may be the same, just an odd angle and I've not seen it in spots like this.
BBA is actually a red algae, but in tanks it is generally very dark green, dark grey, even more brown-black. Like most problem algae (as opposed to common green algae or diatoms even) fish that are said to "eat algae" won't touch this, with two exceptions but that is not the road to go down anyway. Dealing with the cause is how you resolve it, and that involves the light/nutrient balance. You want this in sync for the plants, but not more as that is when problem algae takes advantage. I've never bothered with this algae on wood, only when it appears on plant leaves.
The light involves intensity, spectrum and duration. Nutrients must then balance this--but for the species of plants which have differing needs. This does not look like a new setup, so assuming this, I would start by reducing the duration of the light photoperiod. I have battled this algae a few times over the years, and once I got the balance some six years ago, this algae did not increase and it is basically gone now. Even the extended daylight and brighter daylight entering through windows in summer can affect this.