Studio: creating a new site pulls assistant messages from another site

[kozer]

Fixes https://github.com/Automattic/dotcom-forge/issues/7762

Proposed Changes

This PR fixes a bug where when the user creates a new site, it keeps old selected site messages in AI assistant

Testing Instructions

1. Create a new site.
2. Go to the assistant tab and ask some questions.
3. While being on that tab, add a new site.
4. Ensure that the chat is updated with being in an empty state.
5. Changing back to the old site must still displays the chats.

Pre-merge Checklist

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

[jeroenpf]

These changes work for me. When i create a new site while on the Assistant tab of an existing site, i see the empty state (welcome messages) of AI assistant for the new site.