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/cli.rs

@@ -54,6 +54,10 @@ pub struct Cli {
     #[clap(long = "cd", short = 'C', value_name = "DIR")]
     pub cwd: Option<PathBuf>,
 
+    /// Enable web search (off by default). When enabled, the native Responses `web_search` tool is available to the model (no per‑call approval).
+    #[arg(long = "search", default_value_t = false)]
+    pub web_search: bool,
+
     #[clap(skip)]
     pub config_overrides: CliConfigOverrides,
 }