[EW] AI Assistant should be context aware across pages

Reported by multiple users: you start modifying page 1 using the chat UI. Then you switch page and keep the chat history. If you tell the chat to update content, you'd assume it will update on the new page, but the chat updates the previous page instead.

Either the chat should use the new context, ask for the right context, or we should have a page-based chat.

Source: https://jira.corp.adobe.com/browse/SITES-47107

Start by reproducing the chat UI flow: modify page 1, switch pages, retain the chat history, and request a content update. Trace how the active page context is selected and how chat updates are applied. Done should mean updates target the current page, request the correct context, or use an explicitly page-based chat design agreed by maintainers.

Written by the indexing model from the issue text.