I hate to give griffpatch a poor review, but this add-on does not work. This may be a consequence of the Scratch UI update last year, or an internal interface change, but the add-on opens a tab containing the Scratch homepage when logged in, and a tab containing the login page when not, but does not acknowledge the logged-in-ness of my session. This is even a problem with CorsE (CORS Everywhere) enabled, so I suspect it's a bug with the add-on.

In the new version I still can't get it to register a login. I don't know why. It does seem to clear my unread list on the inbox, which is a bit frustrating (the reason I wanted the add-on was so I could browse my messages with it still remembering where I'd got to on my last session) so it works slightly better than it did.