Session read state should sync across editor and agent window

Does this issue occur when all extensions are disabled?: Yes/No

- VS Code Version:
- OS Version:

Steps to Reproduce:

1. Ask a session in the Agent window `explain fib`
2. Have it complete
3. Check editor window
4. 🐛 Session shows as unread

Reproduce the issue by completing `explain fib` in the Agent window and checking the editor window, first confirming the behavior with extensions disabled. Trace the session read-state handling across both windows; done means a session completed in one window is not incorrectly shown as unread in the other.

Written by the indexing model from the issue text.