- Hide the context bar entirely when there are no context chips
- Render the composer with full rounded corners when it is no longer attached to a context bar

- send the global shortcut to the persistent chat new-session action when the composer has focus
- centralize persistent chat session resets in shared chat state so the shortcut and header button stay in sync
- add chat state coverage for starting and selecting chat sessions

- Extract mention nodes from the chat draft into typed context refs
- Show mentioned sessions, people, and organizations in the context bar while typing
- Persist mention refs on sent messages and render contact/org context into the chat prompt