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/core/src/tools/code_mode.rs

@@ -374,7 +374,10 @@ fn enabled_tool_from_spec(spec: ToolSpec) -> Option<EnabledTool> {
     let (description, kind) = match spec {
         ToolSpec::Function(tool) => (tool.description, CodeModeToolKind::Function),
         ToolSpec::Freeform(tool) => (tool.description, CodeModeToolKind::Freeform),
-        ToolSpec::LocalShell {} | ToolSpec::ImageGeneration { .. } | ToolSpec::WebSearch { .. } => {
+        ToolSpec::LocalShell {}
+        | ToolSpec::ImageGeneration { .. }
+        | ToolSpec::ToolSearch { .. }
+        | ToolSpec::WebSearch { .. } => {
             return None;
         }
     };
@@ -423,25 +426,27 @@ async fn call_nested_tool(
     let router = build_nested_router(&exec).await;
 
     let specs = router.specs();
-    let payload = if let Some((server, tool)) = exec.session.parse_mcp_tool_name(&tool_name).await {
-        match serialize_function_tool_arguments(&tool_name, input) {
-            Ok(raw_arguments) => ToolPayload::Mcp {
-                server,
-                tool,
-                raw_arguments,
-            },
-            Err(error) => return JsonValue::String(error),
-        }
-    } else {
-        match build_nested_tool_payload(&specs, &tool_name, input) {
-            Ok(payload) => payload,
-            Err(error) => return JsonValue::String(error),
-        }
-    };
+    let payload =
+        if let Some((server, tool)) = exec.session.parse_mcp_tool_name(&tool_name, &None).await {
+            match serialize_function_tool_arguments(&tool_name, input) {
+                Ok(raw_arguments) => ToolPayload::Mcp {
+                    server,
+                    tool,
+                    raw_arguments,
+                },
+                Err(error) => return JsonValue::String(error),
+            }
+        } else {
+            match build_nested_tool_payload(&specs, &tool_name, input) {
+                Ok(payload) => payload,
+                Err(error) => return JsonValue::String(error),
+            }
+        };
 
     let call = ToolCall {
         tool_name: tool_name.clone(),
         call_id: format!("{PUBLIC_TOOL_NAME}-{}", uuid::Uuid::new_v4()),
+        tool_namespace: None,
         payload,
     };
     let result = router