Following up on #2371 post commit feedback (#2852)

- Introduce websearch end to complement the begin 
- Moves the logic of adding the sebsearch tool to
create_tools_json_for_responses_api
- Making it the client responsibility to toggle the tool on or off 
- Other misc in #2371 post commit feedback
- Show the query:

<img width="1392" height="151" alt="image"
src="https://github.com/user-attachments/assets/8457f1a6-f851-44cf-bcca-0d4fe460ce89"
/>

codex-rs/mcp-server/src/codex_tool_runner.rs

@@ -274,6 +274,7 @@ async fn run_codex_tool_session_inner(
                     | EventMsg::PatchApplyEnd(_)
                     | EventMsg::TurnDiff(_)
                     | EventMsg::WebSearchBegin(_)
+                    | EventMsg::WebSearchEnd(_)
                     | EventMsg::GetHistoryEntryResponse(_)
                     | EventMsg::PlanUpdate(_)
                     | EventMsg::TurnAborted(_)