Fix TUI context window display before first TokenCount (#13896)

The TUI was showing the raw configured `model_context_window` until the
first
`TokenCount` event arrived, even though core had already emitted the
effective
runtime window on `TurnStarted`. This made the footer, status-line
context
window, and `/status` output briefly inconsistent for models/configs
where the
effective window differs from the configured value, such as the
`gpt-5.4`
1,000,000-token override reported in #13623.

Update the TUI to cache `TurnStarted.model_context_window` immediately
so
pre-token-count displays use the runtime effective window, and add
regression
coverage for the startup path.

---------

Co-authored-by: Charles Cunningham <ccunningham@openai.com>
Co-authored-by: Codex <noreply@openai.com>

codex-rs/tui/src/app.rs

@@ -3316,7 +3316,7 @@ impl App {
     fn handle_codex_event_now(&mut self, event: Event) {
         let needs_refresh = matches!(
             event.msg,
-            EventMsg::SessionConfigured(_) | EventMsg::TokenCount(_)
+            EventMsg::SessionConfigured(_) | EventMsg::TurnStarted(_) | EventMsg::TokenCount(_)
         );
         // This guard is only for intentional thread-switch shutdowns.
         // App-exit shutdowns are tracked by `pending_shutdown_exit_thread_id`
@@ -4805,6 +4805,29 @@ mod tests {
         );
     }
 
+    #[tokio::test]
+    async fn live_turn_started_refreshes_status_line_with_runtime_context_window() {
+        let mut app = make_test_app().await;
+        app.chat_widget
+            .setup_status_line(vec![crate::bottom_pane::StatusLineItem::ContextWindowSize]);
+
+        assert_eq!(app.chat_widget.status_line_text(), None);
+
+        app.handle_codex_event_now(Event {
+            id: "turn-started".to_string(),
+            msg: EventMsg::TurnStarted(TurnStartedEvent {
+                turn_id: "turn-1".to_string(),
+                model_context_window: Some(950_000),
+                collaboration_mode_kind: Default::default(),
+            }),
+        });
+
+        assert_eq!(
+            app.chat_widget.status_line_text(),
+            Some("950K window".into())
+        );
+    }
+
     #[tokio::test]
     async fn open_agent_picker_keeps_missing_threads_for_replay() -> Result<()> {
         let mut app = make_test_app().await;