Allow bool web_search in ToolsToml (#14352)

Summary
- add a custom deserializer so `[tools].web_search` can be a bool
(treated as disabled) or a config object
- extend core and app-server tests to cover bool handling in TOML config

Testing
- Not run (not requested)

codex-rs/app-server/tests/suite/v2/config_rpc.rs

@@ -218,6 +218,38 @@ location = { country = "US", city = "New York", timezone = "America/New_York" }
     Ok(())
 }
 
+#[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+async fn config_read_ignores_bool_web_search_tool_config() -> Result<()> {
+    let codex_home = TempDir::new()?;
+    write_config(
+        &codex_home,
+        r#"
+[tools]
+web_search = true
+"#,
+    )?;
+
+    let mut mcp = McpProcess::new(codex_home.path()).await?;
+    timeout(DEFAULT_READ_TIMEOUT, mcp.initialize()).await??;
+
+    let request_id = mcp
+        .send_config_read_request(ConfigReadParams {
+            include_layers: false,
+            cwd: None,
+        })
+        .await?;
+    let resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(request_id)),
+    )
+    .await??;
+    let ConfigReadResponse { config, .. } = to_response(resp)?;
+
+    assert_eq!(config.tools.expect("tools present").web_search, None,);
+
+    Ok(())
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
 async fn config_read_includes_apps() -> Result<()> {
     let codex_home = TempDir::new()?;