Add websocket telemetry metrics and labels (#10316)

Summary
- expose websocket telemetry hooks through the responses client so
request durations and event processing can be reported
- record websocket request/event metrics and emit runtime telemetry
events that the history UI now surfaces
- improve tests to cover websocket telemetry reporting and guard runtime
summary updates


<img width="824" height="79" alt="Screenshot 2026-01-31 at 5 28 12 PM"
src="https://github.com/user-attachments/assets/ea9a7965-d8b4-4e3c-a984-ef4fdc44c81d"
/>

codex-rs/tui/src/history_cell.rs

@@ -2028,6 +2028,13 @@ fn runtime_metrics_label(summary: RuntimeMetricsSummary) -> Option<String> {
             summary.api_calls.count
         ));
     }
+    if summary.websocket_calls.count > 0 {
+        let duration = format_duration_ms(summary.websocket_calls.duration_ms);
+        parts.push(format!(
+            "WebSocket: {} events send ({duration})",
+            summary.websocket_calls.count
+        ));
+    }
     if summary.streaming_events.count > 0 {
         let duration = format_duration_ms(summary.streaming_events.duration_ms);
         let stream_label = pluralize(summary.streaming_events.count, "Stream", "Streams");
@@ -2037,6 +2044,13 @@ fn runtime_metrics_label(summary: RuntimeMetricsSummary) -> Option<String> {
             summary.streaming_events.count
         ));
     }
+    if summary.websocket_events.count > 0 {
+        let duration = format_duration_ms(summary.websocket_events.duration_ms);
+        parts.push(format!(
+            "{} events received ({duration})",
+            summary.websocket_events.count
+        ));
+    }
     if parts.is_empty() {
         None
     } else {
@@ -2181,15 +2195,25 @@ mod tests {
                 count: 6,
                 duration_ms: 900,
             },
+            websocket_calls: RuntimeMetricTotals {
+                count: 1,
+                duration_ms: 700,
+            },
+            websocket_events: RuntimeMetricTotals {
+                count: 4,
+                duration_ms: 1_200,
+            },
         };
         let cell = FinalMessageSeparator::new(Some(12), Some(summary));
-        let rendered = render_lines(&cell.display_lines(120));
+        let rendered = render_lines(&cell.display_lines(200));
 
         assert_eq!(rendered.len(), 1);
         assert!(rendered[0].contains("Worked for 12s"));
         assert!(rendered[0].contains("Local tools: 3 calls (2.5s)"));
         assert!(rendered[0].contains("Inference: 2 calls (1.2s)"));
+        assert!(rendered[0].contains("WebSocket: 1 events send (700ms)"));
         assert!(rendered[0].contains("Streams: 6 events (900ms)"));
+        assert!(rendered[0].contains("4 events received (1.2s)"));
     }
 
     #[test]