Getting all chats in list

[nakul-py]

Getting the list of all chats in the Open a chat drop-down like as same as we get in @jupyter-chat.

Screencast.From.2025-12-11.22-26-23.mp4

Now this PR also disables the disposing of chat model when chat is closed or moved to main area.

Screencast.From.2025-12-12.08-44-40.mp4

• Closes Improve the list of opened chats #194

cc @brichet @jtpio

[brichet]

Thanks @nakul-py for working on this.

I can see several problems with this implementation, this is why I suggested to implement it in @jupyter/chat:

• there is no way to totally remove a model. This means that if you opened a lot of models, they will all be in the list, even if you don't need it anymore
• from the previous problem, renaming a chat with a former name will not work (and currently it fails silently, maybe we should also fix it separately)
• closing the chat with the cross actually dispose of the model. Currently everything works, nothing append when the model is disposed, but we should use a disposed chat, the behavior can be inconsistent in future.

[nakul-py]

there is no way to totally remove a model. This means that if you opened a lot of models, they will all be in the list, even if you don't need it anymore

This problem will be solved by jupyterlab/jupyter-chat#328