Use @jupyter/chat as chat UI

[brichet]

This would be the first step of #785, before discussing how to use the collaborative chat extension.

Problem

@jupyter/chat package was built mainly by refactoring the code of the jupyter-ai chat component.
One of the idea was to be able to use it in jupyter-ai, while providing a chat component for other possible extensions.

The jupyter-ai chat component has evolved since. If we want the migration to be possible, we need to make sure that all the features of jupyter-ai chat are fulfilled by @jupyter/chat.

Proposed Solution

List all the features of jupyter-ai chat and see if and how they can be implemented in @jupyter/chat, to ensure a smooth migration.

Feel free to update the list below.

cc. @dlqqq @3coins @JasonWeill @ellisonbg

Additional context

• autocompletion Autocomplete UI for slash commands #810
• code toolbar Add code toolbar to Jupyter AI chat #789

[jtpio]

This one (#859) merged a few days ago may also be relevant to jupyterlab/jupyter-chat#52.