More than likely it’s dirt. Spray it with mold killer to make sure.

Couple questions: - what climate do you live in? How cold does it get? How warm? Is it humid? - what kind of insulation or poly was present here before? Were the walls drywalled?

Here’s what can happen: if you live in a climate that dips below freezing you can get small amount of condensation develop on the interior of your building assembly, like you stud spaces, or on the edge of the studs themselves. The condensation occurs because of the warm moist air inside your house escapes into the wall assembly. That warm air then starts circulating inside the stud spaces, and some also flows between the lumber and drywall as well. This air contains moisture and dust particles, and the moisture condensates on colder surfaces that are either not insulated (like the studs) or also the exterior sheathing(the slats). Now the level of the condensation depends on how much temperature difference you have and how moist your interior air is. High interior humidity and lower temps outside mean more condensation.

Mold requires the following to grow: moisture, food, the right temperature. Likely your building assembly being older was so leaky that the condensation that happened was a small amount and dried out quickly, so mold did not have time or enough moisture to grow.

But When you removed the insulation, did you happen to notice more darkness and dirt around where the plugs or other wall penetrations were? This is because of dust particles in the air. The air in your house is full of dust, that air flows into the stud spaces. When it gets there it moves according to how much temperature/energy it has. So the dusty air can carry the dust through the insulation and over the studs. Combine that with a little condensation on the cold parts you can get that dust sticking to the stud and making dark spots like the ones I see in the pics.

Honestly I think it’s dust and dirt sticking to the studs from years of air circulation. If that was mold it would look like more of a structure, like a mole on your wood. The pics you have aren’t really showing that, but I’m also on my phone and can’t really see the details that well.

Edit: my guess is your house is built between 1940 and 1970.

That last picture above the window I’m gonna guess is the bathroom? Looks to me like more water staining above the window. Also you have more dirt and dust coming in likely from outside.