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/handlers/mod.rs

@@ -13,9 +13,9 @@ mod plan;
 mod read_file;
 mod request_permissions;
 mod request_user_input;
-mod search_tool_bm25;
 mod shell;
 mod test_sync;
+mod tool_search;
 pub(crate) mod unified_exec;
 mod view_image;
 
@@ -50,12 +50,12 @@ pub use request_permissions::RequestPermissionsHandler;
 pub(crate) use request_permissions::request_permissions_tool_description;
 pub use request_user_input::RequestUserInputHandler;
 pub(crate) use request_user_input::request_user_input_tool_description;
-pub(crate) use search_tool_bm25::DEFAULT_LIMIT as SEARCH_TOOL_BM25_DEFAULT_LIMIT;
-pub(crate) use search_tool_bm25::SEARCH_TOOL_BM25_TOOL_NAME;
-pub use search_tool_bm25::SearchToolBm25Handler;
 pub use shell::ShellCommandHandler;
 pub use shell::ShellHandler;
 pub use test_sync::TestSyncHandler;
+pub(crate) use tool_search::DEFAULT_LIMIT as TOOL_SEARCH_DEFAULT_LIMIT;
+pub(crate) use tool_search::TOOL_SEARCH_TOOL_NAME;
+pub use tool_search::ToolSearchHandler;
 pub use unified_exec::UnifiedExecHandler;
 pub use view_image::ViewImageHandler;