Problem

Sidebar panel icons, including for panels that are not actively selected, do not have a provision to add a badge or some other visual treatment to suggest that the user should open the sidebar panel and perform some action, such as reading a message or responding to an error.

Proposed Solution

Modify the sidebar widget API to allow for the panel icon to have a badge on it, with some combination of a shape and a text annotation, such as a number. Allow for widgets to dynamically show, hide, or update the badge in response to actions in any part of JupyterLab.

Additional context

See also:

• Notifications when chat UI sends a response message jupyter-ai#111
• https://developer.apple.com/design/human-interface-guidelines/notifications/#Badging