Support all types of search actions (#7061)

Fixes the 

```
{
  "error": {
    "message": "Invalid value: 'other'. Supported values are: 'search', 'open_page', and 'find_in_page'.",
    "type": "invalid_request_error",
    "param": "input[150].action.type",
    "code": "invalid_value"
  }
```
error.


The actual-actual fix here is supporting absent `query` parameter.

codex-rs/core/tests/suite/client.rs

@@ -992,7 +992,7 @@ async fn azure_responses_request_includes_store_and_reasoning_ids() {
         id: Some("web-search-id".into()),
         status: Some("completed".into()),
         action: WebSearchAction::Search {
-            query: "weather".into(),
+            query: Some("weather".into()),
         },
     });
     prompt.input.push(ResponseItem::FunctionCall {