Instead of showing a number next to an object name that represents something, I would like to be able to make it an Icon.
For instance, let's say the badge normally shows a number of rows where the user needs to do something about. But in my case it doesn't matter much if there's is 1 thing or 100 things. So instead of showing  I would like to show an icon. Then when hovering over the icon, it should show an tooltip where I can say to the user why the icon is visible.
Example next to Tab 'File’: