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/exec/src/event_processor_with_human_output.rs

@@ -24,6 +24,7 @@ use codex_core::protocol::StreamErrorEvent;
 use codex_core::protocol::TaskCompleteEvent;
 use codex_core::protocol::TurnAbortReason;
 use codex_core::protocol::TurnDiffEvent;
+use codex_core::protocol::WebSearchBeginEvent;
 use owo_colors::OwoColorize;
 use owo_colors::Style;
 use shlex::try_join;
@@ -361,6 +362,9 @@ impl EventProcessor for EventProcessorWithHumanOutput {
                     }
                 }
             }
+            EventMsg::WebSearchBegin(WebSearchBeginEvent { call_id: _, query }) => {
+                ts_println!(self, "🌐 {query}");
+            }
             EventMsg::PatchApplyBegin(PatchApplyBeginEvent {
                 call_id,
                 auto_approved,