Looks like the mobile site for tracking me is broken on Garmin’s end of things.
(Well, this is lame.)
If you want to kick it old school, the desktop version of the same exact website works just fine.
(Public libraries smell weird.)
I called Garmin’s tech support yesterday. They said they are aware of the issue from other users (iOS and Android both) and expected things to be fixed in a day or two. Fingers crossed.