In all the animations I’ve seen of the orbit around L2, it appears to be elliptical rather than circular. Is that an optical illusion, or is there a benefit to such a path?
AFAIK the elliptical orbit shown is not (easily) possible (source: Kerbal Space Center)
I think they want to show a "vertical" orbit around L2 (where "horizontal" would be earth's orbit around the sun). It's slightly better visible in the youtube movie.