My profile says the last time I visited was June 17th, which is trivially incorrect as I've been here every day.

Is this a bug? Or is it related to my having clicked the "log in anonymously" check box at some point in the past (possibly when I logged in on June 17th)? I can't find any way to tell if that anonymous login state is still active.

I'm going to guess you're still logged in anonymously if you haven't logged out since then. Publicly, the site doesn't consider you logged in if you're anonymous.