Partial AI message from current chat appears in previously opened chat

[HarikeshPratapSingh]

Describe the bug
If an older chat is opened while the AI is still generating a message in the current chat, part of the AI's in-progress message is incorrectly rendered in the older chat.

To Reproduce

1. Open a chat and start an AI message generation.
2. Before the AI finishes responding, navigate to an older chat.
3. Observe that part of the in-progress AI message appears in the older chat.

Expected behavior
Switching to an older chat should not display any portion of the AI message being generated in a different chat. Each chat should only display its own messages.

Screenshots

Chat with the query

Older chat

Desktop

• OS: MacOS 15.6
• Browser: Chrome
• Version: 138.0.7204.184

[codebanesr]

Well, these are not partials, but just the starting of deep research, we need to handle this better