Default message / instructions when opening a new chat

[jtpio]

Problem

Currently the chat panel does not show anything when opening it in a fresh session:

By comparison, Jupyter AI shows a default message to give some guidance:

Proposed Solution

Additional context

To be explored, but we could also consider a more general "overlay", for example like the one in VS Code:

[brichet]

I wonder if it should be configurable in jupyter-chat itself.
There could be an option in the chat widget to add/update a React component or HTMLElement.