[codex] Require model for standalone web search (#25131)

## Why

The standalone `/v1/alpha/search` request now requires a `model`, but
the `web.run` extension currently omits it.

Adds `model` to extension `ToolCall` invocation.

Follow-up to #23823.

## What changed

- Make `SearchRequest.model` required.
- Expose the effective per-turn model on extension tool calls and pass
it in standalone web-search requests.
- Assert the model is forwarded in the app-server round-trip test.

## Testing

- `just test -p codex-api -p codex-tools -p codex-web-search-extension
-p codex-memories-extension -p codex-goal-extension`
- `just test -p codex-core -E
'test(passes_turn_fields_and_scoped_turn_item_emitter_to_extension_call)'`
- `just test -p codex-app-server -E
'test(standalone_web_search_round_trips_encrypted_output)'`

codex-rs/app-server/tests/suite/v2/web_search.rs

@@ -140,6 +140,7 @@ async fn standalone_web_search_round_trips_encrypted_output() -> Result<()> {
     );
 
     let search_body = search_request_body(&server).await?;
+    assert_eq!(search_body["model"], json!("mock-model"));
     assert_eq!(
         search_body["commands"],
         json!({