This began several weeks ago with one of the newer upgrades, but I can’t pinpoint it. Nothing seems to wrong with either the link or the functioning of ST in my browser. I just don’t recognize the icon flag and Mozilla’s help is unhelpful. ST and FF are both current.
We now use syncthing’s fav icon to show some state (syncing, notifications, paused etc), so I cannot explain why your Firefox clinged on to that state for the icon (given there are genuinely no unacknowledged notifications)
The favicon is the little icon that’s shown on the tab which has a website open in it. When you create a bookmark, your browser will save the favicon and display it alongside the bookmark, as your first screenshot shows. It will then periodically update it, based on browser-specific rules.
A few versions ago, Syncthing started using the favicon to indicate things like “Syncting”, “Warnings”, “Stopped”, etc. Your browser happened to update the favicon associated with the bookmark at a point in time when Syncthing had one or more warnings, and so saved the “warning” favicon.
Now it seems to have fetched it again, and this time there were no warnings, so it saved the normal favicon. Nothing to do with the update to 0.13.6.