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/otel/tests/suite/runtime_summary.rs

@@ -11,6 +11,7 @@ use eventsource_stream::Event as StreamEvent;
 use opentelemetry_sdk::metrics::InMemoryMetricExporter;
 use pretty_assertions::assert_eq;
 use std::time::Duration;
+use tokio_tungstenite::tungstenite::Message;
 
 #[test]
 fn runtime_metrics_summary_collects_tool_api_and_streaming_metrics() -> Result<()> {
@@ -43,6 +44,7 @@ fn runtime_metrics_summary_collects_tool_api_and_streaming_metrics() -> Result<(
         "ok",
     );
     manager.record_api_request(1, Some(200), None, Duration::from_millis(300));
+    manager.record_websocket_request(Duration::from_millis(400), None);
     let sse_response: std::result::Result<
         Option<std::result::Result<StreamEvent, eventsource_stream::EventStreamError<&str>>>,
         tokio::time::error::Elapsed,
@@ -53,6 +55,13 @@ fn runtime_metrics_summary_collects_tool_api_and_streaming_metrics() -> Result<(
         retry: None,
     })));
     manager.log_sse_event(&sse_response, Duration::from_millis(120));
+    let ws_response: std::result::Result<
+        Option<std::result::Result<Message, tokio_tungstenite::tungstenite::Error>>,
+        codex_api::ApiError,
+    > = Ok(Some(Ok(Message::Text(
+        r#"{"type":"response.created"}"#.into(),
+    ))));
+    manager.record_websocket_event(&ws_response, Duration::from_millis(80));
 
     let summary = manager
         .runtime_metrics_summary()
@@ -70,6 +79,14 @@ fn runtime_metrics_summary_collects_tool_api_and_streaming_metrics() -> Result<(
             count: 1,
             duration_ms: 120,
         },
+        websocket_calls: RuntimeMetricTotals {
+            count: 1,
+            duration_ms: 400,
+        },
+        websocket_events: RuntimeMetricTotals {
+            count: 1,
+            duration_ms: 80,
+        },
     };
     assert_eq!(summary, expected);