Add background agent notification snapshot

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: stephentoub

test/snapshots/rpc_tasks_and_handlers/should_start_background_agent_and_report_task_details.yaml

@@ -15,6 +15,20 @@ conversations:
         content: Reply with TASK_AGENT_DONE exactly.
       - role: assistant
         content: TASK_AGENT_DONE
+  - messages:
+      - role: system
+        content: ${system}
+      - role: user
+        content: Reply with TASK_AGENT_READY exactly.
+      - role: assistant
+        content: TASK_AGENT_READY
+      - role: user
+        content: |-
+          <system_notification>
+          Agent "sdk-background-agent" (general-purpose) has completed successfully. Use read_agent with agent_id "sdk-background-agent" to retrieve the full results.
+          </system_notification>
+      - role: assistant
+        content: TASK_AGENT_DONE
   - messages:
       - role: system
         content: ${system}