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/tests/common/responses.rs

@@ -494,14 +494,13 @@ pub fn ev_reasoning_text_delta(delta: &str) -> Value {
     })
 }
 
-pub fn ev_web_search_call_added(id: &str, status: &str, query: &str) -> Value {
+pub fn ev_web_search_call_added_partial(id: &str, status: &str) -> Value {
     serde_json::json!({
         "type": "response.output_item.added",
         "item": {
             "type": "web_search_call",
             "id": id,
-            "status": status,
-            "action": {"type": "search", "query": query}
+            "status": status
         }
     })
 }