That Tinycon script is flawed, I've found. It should not be using the logo.og.png file. The problem is that this script renders the open graph image terribly ragged. It is easy to see: if I have to browser tabs open, one on the public side and one on the admin, the admin side renders a very nice tab logo from our favicon file, where the public side looks ragged, like a 16-color GIF image from 15 years ago. I did post on GitHub with the suggestion to force it to use the .ico file, but nobody has responded. Seeing how little the script is updated, I am not holding my breath.
On the left is a proper aliased favicon, where the one on the right is after running through Live Updates:
The add-on uses an outdated version of the script; I tried replacing it with the most recent version, but it looks just as bad.
I'd be happy if I could find a live update add-on that simply changed the text in the browser tab, vs. overlaying the favicon with the count. I don't care how, but as long as the favicon looks cleanly aliased, I'm happy. As it stands, it looks amateurish and embarrassing.