So, I run "GitHub: Open Remote URL in Browser" and get an error message that the branch I'm currently editing has no upstream configured. I mean, this is true, but the behaviour is not at all what I expected.
What you can do in this case is run git log and find literally the next best thing. In most cases by far, it would be good enough. In fact, I can't imagine a single case where a user wouldn't expect this to happen.
I'll certainly implement this myself, most likely as a patch for this plugin, but let me know (in the comments to this) if you want the PR.