Currently TabbedPane tabs can be modified by changing their content text. For example we can mark a tab as "dirty" by adding a "*" to the end of the file name.
More complete styling would allow for example warning and error notifications by, for example, coloring the tab or adding images such as the warning triangle or red dot.
Closing as invalid, as this bug pertains to the old inspector UI and/or its tests.
Please file a new bug (https://www.webkit.org/new-inspector-bug) if the bug/feature/issue is still relevant to WebKit trunk.