feat: search_tool migrate to bring you own tool of Responses API (#14274)

## Why

to support a new bring your own search tool in Responses
API(https://developers.openai.com/api/docs/guides/tools-tool-search#client-executed-tool-search)
we migrating our bm25 search tool to use official way to execute search
on client and communicate additional tools to the model.

## What
- replace the legacy `search_tool_bm25` flow with client-executed
`tool_search`
- add protocol, SSE, history, and normalization support for
`tool_search_call` and `tool_search_output`
- return namespaced Codex Apps search results and wire namespaced
follow-up tool calls back into MCP dispatch

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

@@ -21,6 +21,7 @@ pub(crate) fn attach_item_ids(payload_json: &mut Value, original_items: &[Respon
         | ResponseItem::Message { id: Some(id), .. }
         | ResponseItem::WebSearchCall { id: Some(id), .. }
         | ResponseItem::FunctionCall { id: Some(id), .. }
+        | ResponseItem::ToolSearchCall { id: Some(id), .. }
         | ResponseItem::LocalShellCall { id: Some(id), .. }
         | ResponseItem::CustomToolCall { id: Some(id), .. } = item
         {

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

@@ -641,6 +641,42 @@ mod tests {
         }
     }
 
+    #[tokio::test]
+    async fn parses_tool_search_call_items() {
+        let events = run_sse(vec![
+            json!({
+                "type": "response.output_item.done",
+                "item": {
+                    "type": "tool_search_call",
+                    "call_id": "search-1",
+                    "execution": "client",
+                    "arguments": {
+                        "query": "calendar create",
+                        "limit": 1
+                    }
+                }
+            }),
+            json!({
+                "type": "response.completed",
+                "response": { "id": "resp1" }
+            }),
+        ])
+        .await;
+
+        assert_eq!(events.len(), 2);
+        assert_matches!(
+            &events[0],
+            ResponseEvent::OutputItemDone(ResponseItem::ToolSearchCall {
+                call_id,
+                execution,
+                arguments,
+                ..
+            }) if call_id.as_deref() == Some("search-1")
+                && execution == "client"
+                && arguments == &json!({"query": "calendar create", "limit": 1})
+        );
+    }
+
     #[tokio::test]
     async fn emits_completed_without_stream_end() {
         let completed = json!({