Studio: AssistantIsThinking triggrers across multiple sites

[kozer]

Fixes https://github.com/Automattic/dotcom-forge/issues/7767

Proposed Changes

This PR fixes a bug where when the chat "is thinking" , the loading indicator persists across multiple sites.

Testing Instructions

1. Create two sites.
2. Navigate to Studio AI Assistant tab, of the first one.
3. Submit a prompt to the model; eg: "Give me a 3 paragraph text" ( in order to make the response to slow down and make easier to notice )
4. You should be able to see the "thinking" indicator.
5. Switch to another site.
6. Ensure that the indicator is not there.
7. Now switch to the first one.
8. Ensure that you still see the indicator..

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[jeroenpf]

Works great! When i am waiting for a response i see the loading indicator but when i switch to another site i don't see it.

Also, i tried to have more than one site where I'm waiting for a response and it also works as expected.