The 2.0 reference is available at beta.p5js.org!
I’m not sure specifically whats slowing down your case here, but points currently are drawn differently than strokes. If you use LINES shape mode and add a second point 0.001 away from the original in some axis, do you see any performance difference?
In p5 stroke caps and join styles are all done in the fragment shader so there should be negligible performance difference between them – a round cap is still rendered with just a quad geometry. But currently anyway there is a separate point shader, so trying with LINES mode will use a different rendering pipeline, which is worth testing.