Problem

@jupyter/chat package doesn't provide a multi-chats panel out of the box.

jupyterlab-chat package does, its side panel allows to add/open/close chats, and to move them to the main area.

Proposed Solution

We could make the ChatPanel from jupyterlab-chat generic enough to be provided by @jupyter/chat, and reused in ``jupyterlab-chat`.

Additional context

Related to:

• Ability to create new chats and move them to the main area jupyterlite/ai#111
• Adding New chat button jupyterlite/ai#131