Distinguish turn-start thread persistence (#37926)

## What changed

- Add `PersistContext` to the thread-store persistence contract so stores can
  identify persistence requested immediately before model sampling. A
  `TurnStart` request may be enqueued in the background when later flush and
  shutdown operations fence it and report any failure; all other persistence
  remains synchronous.
- Use the turn-start context only for the initial input of a regular turn, while
  admission acknowledgments, steered input, and other persistence paths keep
  the standard durability behavior.
- Flush pending metadata before turn-start persistence and ensure shutdown is
  still attempted if that metadata update fails.

## Testing

- Verify that developer instructions and user input are persisted before the
  model request completes for a default paginated-history thread.

GitOrigin-RevId: 162f0ec796a61aebe66ca0b909fbcccec3047b85

codex-rs/core/src/tasks/mod.rs

@@ -51,6 +51,7 @@ use codex_protocol::protocol::TurnAbortReason;
 use codex_protocol::protocol::TurnAbortedEvent;
 use codex_protocol::protocol::TurnCompleteEvent;
 use codex_protocol::protocol::WarningEvent;
+use codex_thread_store::PersistContext;
 
 use codex_features::Feature;
 use codex_protocol::error::CodexErrorDetails;
@@ -627,7 +628,13 @@ impl Session {
                 ts.token_usage_at_turn_start.clone(),
             )
         };
-        run_hooks_and_record_inputs(self, &turn_context, &pending_input).await;
+        run_hooks_and_record_inputs(
+            self,
+            &turn_context,
+            &pending_input,
+            PersistContext::Standard,
+        )
+        .await;
         task_ended_before_persistence |= self
             .pending_user_message_admissions
             .complete_task_end(&turn_context.sub_id);