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/tui/src/chatwidget.rs

@@ -28,6 +28,7 @@ use codex_core::protocol::TaskCompleteEvent;
 use codex_core::protocol::TokenUsage;
 use codex_core::protocol::TurnAbortReason;
 use codex_core::protocol::TurnDiffEvent;
+use codex_core::protocol::WebSearchBeginEvent;
 use codex_protocol::parse_command::ParsedCommand;
 use crossterm::event::KeyEvent;
 use crossterm::event::KeyEventKind;
@@ -308,6 +309,11 @@ impl ChatWidget {
         self.defer_or_handle(|q| q.push_mcp_end(ev), |s| s.handle_mcp_end_now(ev2));
     }
 
+    fn on_web_search_begin(&mut self, ev: WebSearchBeginEvent) {
+        self.flush_answer_stream_with_separator();
+        self.add_to_history(history_cell::new_web_search_call(ev.query));
+    }
+
     fn on_get_history_entry_response(
         &mut self,
         event: codex_core::protocol::GetHistoryEntryResponseEvent,
@@ -839,6 +845,7 @@ impl ChatWidget {
             EventMsg::ExecCommandEnd(ev) => self.on_exec_command_end(ev),
             EventMsg::McpToolCallBegin(ev) => self.on_mcp_tool_call_begin(ev),
             EventMsg::McpToolCallEnd(ev) => self.on_mcp_tool_call_end(ev),
+            EventMsg::WebSearchBegin(ev) => self.on_web_search_begin(ev),
             EventMsg::GetHistoryEntryResponse(ev) => self.on_get_history_entry_response(ev),
             EventMsg::McpListToolsResponse(ev) => self.on_list_mcp_tools(ev),
             EventMsg::ShutdownComplete => self.on_shutdown_complete(),