Clicking the widget holding the kernel name could do something useful

I often witness beginners click on the widget displaying the kernel name, expecting something kernel-related to happen. A natural action would be to open a drop-down for changing the kernel. Or maybe the full kernel menu.

No files, tests, or entry points are named; start by locating the widget that displays the kernel name and reviewing its existing interaction behavior. Done means agreeing on and implementing a useful click action, such as opening the kernel dropdown or full kernel menu, with the behavior verified in the notebook UI.

Written by the indexing model from the issue text.