[codex] Support sequential cutoff reasoning summaries (#31306)

## Summary

When enabled for the OpenAI provider, Codex sends
`stream_options.reasoning_summary_delivery = "sequential_cutoff"` on
HTTP and
WebSocket requests, including prewarm, and renders completed summary
sections
from `reasoning_summary_text.done`. Flag-off and non-OpenAI behavior is
unchanged.

## Expected rollout

```text
reasoning 0 added
summary 0 done
summary 1 done
summary 2 starts
summary 2 cancelled / incomplete
reasoning 0 done  <-- cancel summary 2 work and mark it incomplete
message 1 added
message 1 text streams
message 1 completed
```

Depends on
[openai/openai#1096660](https://github.com/openai/openai/pull/1096660).

codex-rs/codex-api/src/sse/responses.rs

@@ -167,6 +167,7 @@ pub struct ResponsesStreamEvent {
     item_id: Option<String>,
     call_id: Option<String>,
     delta: Option<String>,
+    text: Option<String>,
     summary_index: Option<i64>,
     content_index: Option<i64>,
     safety_buffering: Option<Value>,
@@ -358,6 +359,17 @@ pub fn process_responses_event(
                 }));
             }
         }
+        "response.reasoning_summary_text.done" => {
+            if let (Some(item_id), Some(text), Some(summary_index)) =
+                (event.item_id, event.text, event.summary_index)
+            {
+                return Ok(Some(ResponseEvent::ReasoningSummaryDone {
+                    item_id,
+                    text,
+                    summary_index,
+                }));
+            }
+        }
         "response.reasoning_text.delta" => {
             if let (Some(delta), Some(content_index)) = (event.delta, event.content_index) {
                 return Ok(Some(ResponseEvent::ReasoningContentDelta {
@@ -796,6 +808,32 @@ mod tests {
         }
     }
 
+    #[tokio::test]
+    async fn parses_reasoning_summary_done() {
+        let events = run_sse(vec![
+            json!({
+                "type": "response.reasoning_summary_text.done",
+                "item_id": "reasoning-1",
+                "summary_index": 0,
+                "text": "Checking",
+            }),
+            json!({
+                "type": "response.completed",
+                "response": { "id": "resp1" },
+            }),
+        ])
+        .await;
+
+        assert_matches!(
+            &events[0],
+            ResponseEvent::ReasoningSummaryDone {
+                item_id,
+                text,
+                summary_index: 0,
+            } if item_id == "reasoning-1" && text == "Checking"
+        );
+    }
+
     #[tokio::test]
     async fn error_when_missing_completed() {
         let item1 = json!({