Forward turn metadata in standalone web search (#32835)

## What changed

- Add optional serialized Codex turn metadata to extension tool calls.
- Populate it from the current turn context and send it as the
  `x-codex-turn-metadata` header on standalone web search requests.

## Testing

- Extend the app-server web search integration test to verify that client
  metadata, including the model ID, reaches the standalone search request.

GitOrigin-RevId: c0950108d89a1d317ac94ccd23efcee72fffc6f0

codex-rs/tools/src/tool_call.rs

@@ -92,6 +92,7 @@ pub struct ToolCall {
     pub call_id: String,
     pub tool_name: ToolName,
     pub model: String,
+    pub codex_turn_metadata: Option<String>,
     pub truncation_policy: TruncationPolicy,
     pub conversation_history: ConversationHistory,
     pub turn_item_emitter: Arc<dyn TurnItemEmitter>,
@@ -106,6 +107,10 @@ impl std::fmt::Debug for ToolCall {
             .field("call_id", &self.call_id)
             .field("tool_name", &self.tool_name)
             .field("model", &self.model)
+            .field(
+                "has_codex_turn_metadata",
+                &self.codex_turn_metadata.is_some(),
+            )
             .field("truncation_policy", &self.truncation_policy)
             .field("conversation_history", &self.conversation_history)
             .field("turn_item_emitter", &"<host turn item emitter>")