I’ve experimented with using arrows next the logo similar to how wifi / network icons sometimes show their connectivity status, but as generalmanager says it add another icon(s) next to it and might be confusing. Still experimenting with it though using them in a corner.
Since I’m using Gnome Shell as my desktop I found another interesting extension. I actually use(d) syncthing GTK just for it’s icon in the system tray anyway, so the original web interface itself is fine by me for configuration purposes. This extension doesn’t show any state however, so I decided to continue working on it myself.
This extension actually proves my point though, the icon looks very badly and even he enlarged the node circles and the lines as well, in the original icon the nodes are barely distinguishable.