Track root turns across delegated Codex requests (#38232)

## Why

`parent_turn_id` identifies the immediate caller of a nested request, but not the
top-level turn that initiated a multi-level chain of work.

## What changed

- Add `root_turn_id` to turn state, submissions, and Responses API metadata.
- Propagate the root through spawned agents, delegated work, review sessions, and
  turn-triggering inter-agent messages.
- Omit the root when background work has no user turn or combined input makes the
  root ambiguous.

## Testing

Added coverage for nested agent resumes, reviews, mailbox delivery, steered input,
and reserved metadata handling.

GitOrigin-RevId: 60057db2ee81f4efefa946a9f63c74ff98b93929

codex-rs/mcp-server/src/codex_tool_runner.rs

@@ -114,6 +114,7 @@ pub async fn run_codex_tool_session(
         client_user_message_id: None,
         trace: None,
         parent_turn_id: None,
+        root_turn_id: None,
     };
 
     if let Err(e) = thread.submit_with_id(submission).await {
@@ -159,6 +160,7 @@ pub async fn run_codex_tool_session_reply(
             client_user_message_id: None,
             trace: None,
             parent_turn_id: None,
+            root_turn_id: None,
         })
         .await
     {

codex-rs/mcp-server/src/message_processor.rs

@@ -565,6 +565,7 @@ impl MessageProcessor {
                 client_user_message_id: None,
                 trace: None,
                 parent_turn_id: None,
+                root_turn_id: None,
             })
             .await
         {