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/app-server-protocol/schema/json/EventMsg.json

@@ -5286,6 +5286,12 @@
             "name": {
               "type": "string"
             },
+            "namespace": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
             "type": {
               "enum": [
                 "function_call"
@@ -5303,6 +5309,47 @@
           "title": "FunctionCallResponseItem",
           "type": "object"
         },
+        {
+          "properties": {
+            "arguments": true,
+            "call_id": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
+            "execution": {
+              "type": "string"
+            },
+            "id": {
+              "type": [
+                "string",
+                "null"
+              ],
+              "writeOnly": true
+            },
+            "status": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
+            "type": {
+              "enum": [
+                "tool_search_call"
+              ],
+              "title": "ToolSearchCallResponseItemType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "arguments",
+            "execution",
+            "type"
+          ],
+          "title": "ToolSearchCallResponseItem",
+          "type": "object"
+        },
         {
           "properties": {
             "call_id": {
@@ -5392,6 +5439,41 @@
           "title": "CustomToolCallOutputResponseItem",
           "type": "object"
         },
+        {
+          "properties": {
+            "call_id": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
+            "execution": {
+              "type": "string"
+            },
+            "status": {
+              "type": "string"
+            },
+            "tools": {
+              "items": true,
+              "type": "array"
+            },
+            "type": {
+              "enum": [
+                "tool_search_output"
+              ],
+              "title": "ToolSearchOutputResponseItemType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "execution",
+            "status",
+            "tools",
+            "type"
+          ],
+          "title": "ToolSearchOutputResponseItem",
+          "type": "object"
+        },
         {
           "properties": {
             "action": {