Add multi-conversation management

[michaelchia]

Problem

I would like to reenter previous conversations.

Proposed Solution

Proposal is to add a couple more buttons at the top to start a new conversation (from #616) and to visit the past conversations.

Upon clicking that middle button it could just show a list of past conversations where the text is the first message of the conversation. It shows when the last message was sent and provides a delete button. Also, it also provides a 'new conversation' button and 'delete all' button.

Potential future enhancement (not shown):

• search bar
• recording, indicating and setting last used model for each conversation
  • if users tend to use different models for tasks
  • personally, I intend to create custom "models" with special behaviour (RAG or agent flows)

I am absolutely terrible at UI/UX so please improve upon this.

Additional context

This is a follow-up from #616

[labarba]

Would y'all consider a simpler solution? I rather think the feature creep here could start making the UI/UX cumbersome. We already have an /export command that outputs a full record of the chat in Markdown. I love this! What about adding an /import command that loads a past chat with the file name? The user may continue chatting from there... It just requires users to do their own data management of chat histories in local folders—which sounds good to me. One can organize chat files by personal projects or topics, rather than the chronological chat list on the UI, which grows unwieldy. One can even share them with others, post them online, archive them with a DOI, etc.

[krassowski]

Of note https://github.com/jupyterlab/jupyter-chat natively supports opening conversation history from UI.

[krassowski]

I don't know if this should be a separate issue, but I wanted to note that chat GPT also has branching on conversations exposed to UI as little < and > buttons which appear after user edits a message:

I would like to replicate this behaviour when implementing #339