Clicking on tags broken?
What "Featured tab"? How/why did this happen?
This is basically the same issue as explained here, here you noticing moreso that the tab is missing rather than the lack of tagged questions. Which, in itself, is the reason why the tab is missing.
The featured tab is only shown if there exist featured questions to look at under that tag. If there are none, it's removed from the UI to prevent people from haplessly wandering into it.
However, the Stack Exchange Sites track whichever tab you were last browsing as you navigate the site. That way, as you change tags, it'll preserve the tab. This has a consequence of preserving the featured tab even when the next tag has no bounty questions, and is the only method outside of URL manipulation to access this non-existent tab.