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/core/src/client_common.rs

@@ -95,7 +95,6 @@ pub enum ResponseEvent {
     ReasoningSummaryPartAdded,
     WebSearchCallBegin {
         call_id: String,
-        query: Option<String>,
     },
 }