fix: handle all web_search actions and in progress invocations (#9960)

### Summary
- Parse all `web_search` tool actions (`search`, `find_in_page`,
`open_page`).
- Previously we only parsed + displayed `search`, which made the TUI
appear to pause when the other actions were being used.
- Show in progress `web_search` calls as `Searching the web`
  - Previously we only showed completed tool calls

<img width="308" height="149" alt="image"
src="https://github.com/user-attachments/assets/90a4e8ff-b06a-48ff-a282-b57b31121845"
/>

### Tests
Added + updated tests, tested locally

### Follow ups
Update VSCode extension to display these as well

codex-rs/exec/src/exec_events.rs

@@ -1,3 +1,4 @@
+use codex_protocol::models::WebSearchAction;
 use mcp_types::ContentBlock as McpContentBlock;
 use serde::Deserialize;
 use serde::Serialize;
@@ -280,7 +281,9 @@ pub struct McpToolCallItem {
 /// A web search request.
 #[derive(Debug, Clone, Serialize, Deserialize, PartialEq, TS)]
 pub struct WebSearchItem {
+    pub id: String,
     pub query: String,
+    pub action: WebSearchAction,
 }
 
 /// An error notification.