Track image generation request IDs in analytics (#40714)

## What changed

- Read `x-codex-imagegen-request-id` from image generation and edit responses.
- Propagate the ID to `codex_image_generation_event` analytics.
- Keep the ID in process only, excluding it from extension item serialization, generated types, app-server wire data, and rollout history.

## Testing

- Cover response-header extraction and missing-header behavior in the images client.
- Verify end-to-end analytics emission and the unchanged image-generation item wire shape.

GitOrigin-RevId: 9b8e09b7d655c0c2faa84f0eee99aabae583668d

codex-rs/ext/items/src/tests.rs

@@ -17,6 +17,7 @@ fn completed_image_generation_item() -> ExtensionItem {
         transparent_background: None,
         failure: None,
         saved_path: None,
+        imagegen_request_id: None,
     })
 }
 
@@ -89,6 +90,25 @@ fn image_generation_transparency_is_optional_in_typescript() {
     );
 }
 
+#[test]
+fn image_generation_request_id_stays_internal() {
+    let ExtensionItem::ImageGeneration(mut image) = completed_image_generation_item() else {
+        panic!("expected image-generation item");
+    };
+    image.imagegen_request_id = Some("req-imagegen-123".to_string());
+    let item = ExtensionItem::ImageGeneration(image);
+    let value = serde_json::to_value(&item).expect("serialize extension item");
+
+    assert!(value.get("imagegenRequestId").is_none());
+    let ExtensionItem::ImageGeneration(round_tripped) =
+        serde_json::from_value::<ExtensionItem>(value).expect("deserialize extension item")
+    else {
+        panic!("expected image-generation item");
+    };
+    assert_eq!(round_tripped.imagegen_request_id, None);
+    assert!(!ImageGenerationItem::inline().contains("imagegenRequestId"));
+}
+
 #[test]
 fn web_search_item_preserves_stable_wire_shape() {
     let item = ExtensionItem::WebSearch(WebSearchItem {