Add realtime silence tool (#18635)

## Summary

Adds a second realtime v2 function tool, `remain_silent`, so the
realtime model has an explicit non-speaking action when the
collaboration mode or latest context says it should not answer aloud.
This is stacked on #18597.

## Design

- Advertise `remain_silent` alongside `background_agent` in realtime v2
conversational sessions.
- Parse `remain_silent` function calls into a typed
`RealtimeEvent::NoopRequested` event.
- Have core answer that function call with an empty
`function_call_output` and deliberately avoid `response.create`, so no
follow-up realtime response is requested.
- Keep the event hidden from app-server/TUI surfaces; it is operational
plumbing, not user-visible conversation content.

codex-rs/core/src/realtime_conversation.rs

@@ -1105,7 +1105,7 @@ async fn handle_handoff_output(
                 output_text,
             } => {
                 writer
-                    .send_conversation_handoff_append(handoff_id, output_text)
+                    .send_conversation_function_call_output(handoff_id, output_text)
                     .await
             }
         },
@@ -1129,7 +1129,7 @@ async fn handle_handoff_output(
                 output_text: _,
             } => {
                 if let Err(err) = writer
-                    .send_conversation_handoff_append(
+                    .send_conversation_function_call_output(
                         handoff_id,
                         REALTIME_V2_HANDOFF_COMPLETE_ACKNOWLEDGEMENT.to_string(),
                     )
@@ -1263,7 +1263,7 @@ async fn handle_realtime_server_event(
                     match active_handoff {
                         Some(_) => {
                             if let Err(err) = writer
-                                .send_conversation_handoff_append(
+                                .send_conversation_function_call_output(
                                     handoff.handoff_id.clone(),
                                     REALTIME_V2_STEER_ACKNOWLEDGEMENT.to_string(),
                                 )
@@ -1292,6 +1292,27 @@ async fn handle_realtime_server_event(
             }
             false
         }
+        RealtimeEvent::NoopRequested(noop) => {
+            *output_audio_state = None;
+
+            match session_kind {
+                RealtimeSessionKind::V1 => {}
+                RealtimeSessionKind::V2 => {
+                    if let Err(err) = writer
+                        .send_conversation_function_call_output(noop.call_id.clone(), String::new())
+                        .await
+                    {
+                        let mapped_error = map_api_error(err);
+                        warn!("failed to send realtime noop function output: {mapped_error}");
+                        let _ = events_tx
+                            .send(RealtimeEvent::Error(mapped_error.to_string()))
+                            .await;
+                        return Err(mapped_error.into());
+                    }
+                }
+            }
+            false
+        }
         RealtimeEvent::Error(_) => true,
         RealtimeEvent::SessionUpdated { session_id, .. } => {
             info!(realtime_session_id = %session_id, "realtime session updated");