standalone websearch extension (#23823)

## Summary

Add the extension-backed standalone `web.run` tool so Codex can call the
standalone search endpoint through the `codex-api` search client and
return its encrypted output to Responses.

- gate the new tool behind `standalone_web_search`
- install the extension in the app-server thread registry and hide
hosted `web_search` when standalone search is enabled for OpenAI
providers so the two paths stay mutually exclusive
- build search context from persisted history using a small tail
heuristic: previous user message, assistant text between the last two
user turns capped at about 1k tokens, and current user message

## Test Plan

- `cargo test -p codex-web-search-extension`
- `cargo test -p codex-api`
- `cargo test -p codex-core
hosted_tools_follow_provider_auth_model_and_config_gates`

codex-rs/tools/src/lib.rs

@@ -8,6 +8,7 @@ mod image_detail;
 mod json_schema;
 mod mcp_tool;
 mod request_plugin_install;
+mod response_history;
 mod responses_api;
 mod tool_call;
 mod tool_config;
@@ -45,6 +46,8 @@ pub use request_plugin_install::RequestPluginInstallResult;
 pub use request_plugin_install::all_requested_connectors_picked_up;
 pub use request_plugin_install::build_request_plugin_install_elicitation_request;
 pub use request_plugin_install::verified_connector_install_completed;
+pub use response_history::retain_tail_from_last_n_user_messages;
+pub use response_history::truncate_assistant_output_text_to_token_budget;
 pub use responses_api::FreeformTool;
 pub use responses_api::FreeformToolFormat;
 pub use responses_api::LoadableToolSpec;