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_runner.rs

@@ -272,6 +272,7 @@ async fn run_codex_tool_session_inner(
                     | EventMsg::PatchApplyBegin(_)
                     | EventMsg::PatchApplyEnd(_)
                     | EventMsg::TurnDiff(_)
+                    | EventMsg::WebSearchBegin(_)
                     | EventMsg::GetHistoryEntryResponse(_)
                     | EventMsg::PlanUpdate(_)
                     | EventMsg::TurnAborted(_)