Earlier quoted context omitted.
Canvas can't "see the output", it only sees what is drawn in it (which is not a set of HTML tags, it's JS commands). The screen recording/screen sharing API can be used for this but security is the reason you have to give explicit permission to the site before it can do this.
IIRC, Firefox had a bug where this exact scenario was possible, I think you needed to embed the link in html embedded inside an SVG, which was displayed in the canvas, and then access the bitmap. You could e.g. make the link black if visited and white otherwise, and then the number of white versus black pixels in the bitmap would tell you whether the link was visited or not. There was also that asteroids game / captc…
If you go back far enough there weren't even protections against this sort of thing at all! E.g. you could just say a visited link style was 1px taller then measure that. The protections had to be added in after the fact (often with special case logic for what's allowed to be styled or read on :visited) once security became a major concern!