Make changes to the webui to use local-site APIs

The webui wasn't calling into the correct API paths for things related to review
requests. I'm not entirely positive that I caught everything, but this seems to
have fixed screenshot upload and commenting, review commenting, diff commenting
and replies to all of the above.

Ran through a bunch of actions relating to an open, local-site-ed review request,
including creating reviews, comments, and replies.