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/core/src/tasks/mod.rs

@@ -317,12 +317,23 @@ impl Session {
             .await
             .clear_turn(&turn_context.sub_id);
 
-        let (pending_items, parent_turn_id) =
+        let (pending_items, parent_turn_id, root_turn_id) =
             self.input_queue.get_pending_input(&self.active_turn).await;
-        if let (MailboxParentProvenance::Attribute, Some(id)) =
-            (mailbox_parent_provenance, parent_turn_id)
+        if let MailboxParentProvenance::Attribute = mailbox_parent_provenance {
+            if let Some(id) = parent_turn_id {
+                turn_context.turn_metadata_state.set_parent_turn_id(id);
+            }
+            if let Some(id) = root_turn_id {
+                turn_context.turn_metadata_state.set_root_turn_id(id);
+            }
+        } else if pending_items.iter().any(|item| {
+            matches!(
+                item,
+                TurnInput::InterAgentCommunication(communication) if communication.trigger_turn
+            )
+        }) && turn_context.turn_metadata_state.root_turn_id() != root_turn_id
         {
-            turn_context.turn_metadata_state.set_parent_turn_id(id);
+            turn_context.turn_metadata_state.mark_root_turn_ambiguous();
         }
         let turn_state = {
             let mut active = self.active_turn.lock().await;