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/thread-store/src/lib.rs

@@ -32,6 +32,7 @@ pub use local::RolloutMigrationReport;
 pub use local::RolloutMigrationStatus;
 pub use queue_store::LocalQueueStore;
 pub use queue_store::QueueStore;
+pub use store::PersistContext;
 pub use store::ThreadStore;
 pub use store::ThreadStoreFuture;
 pub use thread_sections::CreateThreadSectionParams;