I decided to build a pure JS plugin for TT-RSS for fun and have been using it since quite a while, maybe someone else has a use for this. It adds a simple badge counter to the favicon every time the unread items count changes.
The source code and released versions are available on GitHub. The newest version is 1.1.0.
To install the plugin, simply download the newest release, unzip it to your plugins folder and activate the plugin in your users settings.
As a side note: There already is another plugin mentioned in these forums that does the same thing – the difference is only in the implementation… the linked plugin checks the title for the unread count every second, my plugin uses the MutationObserver API to update the badge only if the title of the tab actually changes. I personally think my plugin is a cleaner and better implementation because of this, but MutationObserver is only available IE10+ (and all other modern browsers).