Dedicate one set of chat handlers per room

[dlqqq]

Description

• Makes chat handlers non-singletons in Jupyter AI. Each chat handler is dedicated to at most 1 YChat instance.
• Makes YChat an instance attribute instead of a local variable that gets forwarded across methods.
• Reverts most changes to chat handlers (except for the base class).

Demo

Screen.Recording.2024-12-04.at.11.03.06.AM.mov

[brichet]

Thanks @dlqq, this looks great and should considerably reduce the diffs in jupyterlab#1043.

I have some comments/questions below.

[dlqqq]

@brichet Addressed your comments. As for the ychats_by_room dict, we can remove that later. It has a tiny memory footprint, and there could be a future use-case for caching get_room() calls.