[eyelidlessness]

Really? Because I thought of one in the time it took to read this comment. Your extension has access to the page contents, which you can use to determine the username. It’s right in the nav. You can validate that it’s authenticated by a quick look at the profile link to see that it’s editable. Cache that boolean with a hash of the cookie for subsequent validation and you’re all done, without sending anything to your own server.