fix(coach): deep-link the proactive nudge to its conversation

The bottom-right launcher opened a blank new chat on an unread proactive
message instead of the thread the Coach wrote. Return the owning
conversation id from the nudge-status endpoint, have the launcher open
/coach?c=<id> on the unread path, and stamp the same deep link on the push
metadata so the notification lands in the exact conversation rather than
relying on a most-recent heuristic.

docs/api/openapi.yaml

@@ -16654,9 +16654,16 @@ components:
             unread:
               type: boolean
               description: True when that message is newer than the last time the caller opened the Coach.
+            conversationId:
+              anyOf:
+                - type: string
+                - type: "null"
+              description: Conversation holding the newest assistant message; null when none exists. The client deep-links into it
+                (`/coach?c=<id>`) on the unread path.
           required:
             - nudgedAt
             - unread
+            - conversationId
           additionalProperties: false
         error:
           type: "null"