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/protocol/src/protocol.rs

@@ -443,6 +443,8 @@ pub enum EventMsg {
 
     WebSearchBegin(WebSearchBeginEvent),
 
+    WebSearchEnd(WebSearchEndEvent),
+
     /// Notification that the server is about to execute a command.
     ExecCommandBegin(ExecCommandBeginEvent),
 
@@ -675,6 +677,11 @@ impl McpToolCallEndEvent {
 #[derive(Debug, Clone, Deserialize, Serialize)]
 pub struct WebSearchBeginEvent {
     pub call_id: String,
+}
+
+#[derive(Debug, Clone, Deserialize, Serialize)]
+pub struct WebSearchEndEvent {
+    pub call_id: String,
     pub query: String,
 }