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/codex-api/src/telemetry.rs

@@ -1,3 +1,4 @@
+use crate::error::ApiError;
 use codex_client::Request;
 use codex_client::RequestTelemetry;
 use codex_client::Response;
@@ -10,6 +11,8 @@ use std::future::Future;
 use std::sync::Arc;
 use std::time::Duration;
 use tokio::time::Instant;
+use tokio_tungstenite::tungstenite::Error;
+use tokio_tungstenite::tungstenite::Message;
 
 /// Generic telemetry.
 pub trait SseTelemetry: Send + Sync {
@@ -28,6 +31,17 @@ pub trait SseTelemetry: Send + Sync {
     );
 }
 
+/// Telemetry for Responses WebSocket transport.
+pub trait WebsocketTelemetry: Send + Sync {
+    fn on_ws_request(&self, duration: Duration, error: Option<&ApiError>);
+
+    fn on_ws_event(
+        &self,
+        result: &Result<Option<Result<Message, Error>>, ApiError>,
+        duration: Duration,
+    );
+}
+
 pub(crate) trait WithStatus {
     fn status(&self) -> StatusCode;
 }