Add web search tool (#2371)

Adds web_search tool, enabling the model to use Responses API web_search
tool.
- Disabled by default, enabled by --search flag
- When --search is passed, exposes web_search_request function tool to
the model, which triggers user approval. When approved, the model can
use the web_search tool for the remainder of the turn
<img width="1033" height="294" alt="image"
src="https://github.com/user-attachments/assets/62ac6563-b946-465c-ba5d-9325af28b28f"
/>

---------

Co-authored-by: easong-openai <easong@openai.com>

codex-rs/mcp-server/src/codex_tool_config.rs

@@ -163,6 +163,7 @@ impl CodexToolCallParam {
             include_apply_patch_tool: None,
             disable_response_storage: None,
             show_raw_agent_reasoning: None,
+            tools_web_search_request: None,
         };
 
         let cli_overrides = cli_overrides