I don’t mean to post to an old post like this, but is this different now?
I can use the annotate on the surface just fine.
If I do it with the grease pencil it gets really weird…
ANNOTATE:

GREASE:
Blue when not snapping

When you turn Stroke Placement from Origin to Surface however…

It’s somehow thicker, and quite a bit off the model.
Has annotate improved for this use? It’s quite easier out of the box and can be done in edit mode unlike grease pencil it seems.
The grease pencil has always confused me XD