If it were black algae, rubbing a trichlor puck on it for a few minutes would remove the black staining. It wouldn’t necessarily get rid of the BA because that form of algae tends to develop hyphae deep into the plaster, but it would make it disappear for a bit.
Could also be dirty calcium scale. Calcium carbonate is white in its pure form but it can pick up and entrain a lot of dirt and silt suspended in the pool water. I believe the Jacks Stain Kit lumps scale and copper into the same test. Sulfamic acid is less aggressive towards calcium scale than copper stains.
If it’s scale, you can take a wet/dry sanding sponge, medium or fine grit and hit an inconspicuous spot with it. See if that polishes the plaster clean.