[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/tools/src/tool_call.rs

@@ -87,6 +87,7 @@ pub struct ToolCall {
     pub turn_id: String,
     pub call_id: String,
     pub tool_name: ToolName,
+    pub model: String,
     pub truncation_policy: TruncationPolicy,
     pub conversation_history: ConversationHistory,
     pub turn_item_emitter: Arc<dyn TurnItemEmitter>,
@@ -99,6 +100,7 @@ impl std::fmt::Debug for ToolCall {
             .field("turn_id", &self.turn_id)
             .field("call_id", &self.call_id)
             .field("tool_name", &self.tool_name)
+            .field("model", &self.model)
             .field("truncation_policy", &self.truncation_policy)
             .field("conversation_history", &self.conversation_history)
             .field("turn_item_emitter", &"<host turn item emitter>")