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/history_cell.rs

@@ -445,6 +445,12 @@ pub(crate) fn new_active_mcp_tool_call(invocation: McpInvocation) -> PlainHistor
     PlainHistoryCell { lines }
 }
 
+pub(crate) fn new_web_search_call(query: String) -> PlainHistoryCell {
+    let lines: Vec<Line<'static>> =
+        vec![Line::from(""), Line::from(vec!["🌐 ".into(), query.into()])];
+    PlainHistoryCell { lines }
+}
+
 /// If the first content is an image, return a new cell with the image.
 /// TODO(rgwood-dd): Handle images properly even if they're not the first result.
 fn try_new_completed_mcp_tool_call_with_image_output(