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/app-server/src/external_agent_migration/session_importer.rs

@@ -36,6 +36,7 @@ use codex_rollout::RolloutItem;
 use codex_rollout::is_persisted_rollout_item;
 use codex_thread_store::AppendThreadItemsParams;
 use codex_thread_store::CreateThreadParams;
+use codex_thread_store::PersistContext;
 use codex_thread_store::ThreadMetadataPatch;
 use codex_thread_store::ThreadPersistenceMetadata;
 use codex_thread_store::ThreadStore;
@@ -576,7 +577,7 @@ impl ExternalAgentSessionImporter {
                 )
             })?;
         self.thread_store
-            .persist_thread(thread_id)
+            .persist_thread(thread_id, PersistContext::Standard)
             .await
             .map_err(|err| {
                 SessionImportStepFailure::new(