[core] Support interleaved response items (#30876)

## Summary

- preserve reasoning item IDs on summary part and text delta events
- track streamed response items by ID so reasoning summaries can
continue after later items begin
- keep TUI output complete and deduplicated when reasoning and
final-answer events interleave

## Stack

- **1/2: this PR — interleaved item support**
- 2/2: #30752 — wire reasoning summary delivery configuration through
the CLI and app-server

## Validation

- just test -p codex-api preserves_reasoning_summary_item_ids
- just test -p codex-core
interleaved_reasoning_summary_events_keep_reasoning_item_metadata
- just test -p codex-tui
live_reasoning_summary_is_not_rendered_twice_when_item_completes
- just fix -p codex-api -p codex-core -p codex-tui
- just fmt

codex-rs/codex-api/src/common.rs

@@ -101,6 +101,7 @@ pub enum ResponseEvent {
         delta: String,
     },
     ReasoningSummaryDelta {
+        item_id: String,
         delta: String,
         summary_index: i64,
     },
@@ -109,6 +110,7 @@ pub enum ResponseEvent {
         content_index: i64,
     },
     ReasoningSummaryPartAdded {
+        item_id: String,
         summary_index: i64,
     },
     RateLimits(RateLimitSnapshot),

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

@@ -351,8 +351,11 @@ pub fn process_responses_event(
             }
         }
         "response.reasoning_summary_text.delta" => {
-            if let (Some(delta), Some(summary_index)) = (event.delta, event.summary_index) {
+            if let (Some(item_id), Some(delta), Some(summary_index)) =
+                (event.item_id, event.delta, event.summary_index)
+            {
                 return Ok(Some(ResponseEvent::ReasoningSummaryDelta {
+                    item_id,
                     delta,
                     summary_index,
                 }));
@@ -444,8 +447,9 @@ pub fn process_responses_event(
             }
         }
         "response.reasoning_summary_part.added" => {
-            if let Some(summary_index) = event.summary_index {
+            if let (Some(item_id), Some(summary_index)) = (event.item_id, event.summary_index) {
                 return Ok(Some(ResponseEvent::ReasoningSummaryPartAdded {
+                    item_id,
                     summary_index,
                 }));
             }
@@ -796,6 +800,44 @@ mod tests {
         }
     }
 
+    #[tokio::test]
+    async fn preserves_reasoning_summary_item_ids() {
+        let events = run_sse(vec![
+            json!({
+                "type": "response.reasoning_summary_part.added",
+                "item_id": "reasoning-1",
+                "summary_index": 0
+            }),
+            json!({
+                "type": "response.reasoning_summary_text.delta",
+                "item_id": "reasoning-1",
+                "summary_index": 0,
+                "delta": "Checking"
+            }),
+            json!({
+                "type": "response.completed",
+                "response": { "id": "resp1" }
+            }),
+        ])
+        .await;
+
+        assert_matches!(
+            &events[0],
+            ResponseEvent::ReasoningSummaryPartAdded {
+                item_id,
+                summary_index: 0,
+            } if item_id == "reasoning-1"
+        );
+        assert_matches!(
+            &events[1],
+            ResponseEvent::ReasoningSummaryDelta {
+                item_id,
+                delta,
+                summary_index: 0,
+            } if item_id == "reasoning-1" && delta == "Checking"
+        );
+    }
+
     #[tokio::test]
     async fn error_when_missing_completed() {
         let item1 = json!({