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/core/src/lib.rs

@@ -69,6 +69,7 @@ mod event_mapping;
 pub mod review_format;
 pub mod review_prompts;
 mod thread_manager;
+pub mod web_search;
 pub use codex_protocol::protocol::InitialHistory;
 pub use thread_manager::NewThread;
 pub use thread_manager::ThreadManager;