Reset app-server turn summaries when a turn starts (#60434)

## Why

An error recorded before a turn starts can cause a successful turn to be reported as failed.

## What changed

Reset `TurnSummary` on `TurnStarted`, preserving the new turn's `started_at` timestamp while clearing accumulated errors, command start times, and the last agent message.

## Testing

Extend turn completion tests to cover clearing an error recorded before turn start and retaining an error recorded during the turn.

GitOrigin-RevId: 19989b55d20df7b9a265bd0a1dfb3f00b6e8a9c5

codex-rs/app-server/src/bespoke_event_handling.rs

@@ -3492,6 +3492,17 @@ mod tests {
             ThreadId::new(),
         );
         let thread_state = new_thread_state();
+        handle_error(
+            conversation_id,
+            TurnError {
+                misalignment: None,
+                message: "conversation is not running".to_string(),
+                codex_error_info: Some(V2CodexErrorInfo::Other),
+                additional_details: None,
+            },
+            &thread_state,
+        )
+        .await;
         let event = turn_complete_event(&event_turn_id);
         {
             let mut state = thread_state.lock().await;
@@ -3648,6 +3659,18 @@ mod tests {
         let conversation_id = ThreadId::new();
         let event_turn_id = "complete_err1".to_string();
         let thread_state = new_thread_state();
+        thread_state.lock().await.track_current_turn_event(
+            &event_turn_id,
+            &EventMsg::TurnStarted(codex_protocol::protocol::TurnStartedEvent {
+                turn_attribution: None,
+                turn_id: event_turn_id.clone(),
+                root_turn_id: None,
+                trace_id: None,
+                started_at: Some(42),
+                model_context_window: None,
+                collaboration_mode_kind: Default::default(),
+            }),
+        );
         handle_error(
             conversation_id,
             TurnError {

codex-rs/app-server/src/thread_state.rs

@@ -235,7 +235,10 @@ impl ThreadState {
 
     pub(crate) fn track_current_turn_event(&mut self, event_turn_id: &str, event: &EventMsg) {
         if let EventMsg::TurnStarted(payload) = event {
-            self.turn_summary.started_at = payload.started_at;
+            self.turn_summary = TurnSummary {
+                started_at: payload.started_at,
+                ..Default::default()
+            };
         }
         if let EventMsg::ItemCompleted(payload) = event
             && let CoreTurnItem::AgentMessage(item) = &payload.item