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/in_memory.rs

@@ -26,6 +26,7 @@ use crate::DeleteThreadParams;
 use crate::ListThreadsParams;
 use crate::LoadThreadHistoryParams;
 use crate::MoveThreadToSectionParams;
+use crate::PersistContext;
 use crate::ReadThreadByRolloutPathParams;
 use crate::ReadThreadParams;
 use crate::ResumeThreadParams;
@@ -816,7 +817,11 @@ impl ThreadStore for InMemoryThreadStore {
         Box::pin(InMemoryThreadStore::append_items(self, params))
     }
 
-    fn persist_thread(&self, _thread_id: ThreadId) -> ThreadStoreFuture<'_, ()> {
+    fn persist_thread(
+        &self,
+        _thread_id: ThreadId,
+        _context: PersistContext,
+    ) -> ThreadStoreFuture<'_, ()> {
         Box::pin(async move {
             self.state.lock().await.calls.persist_thread += 1;
             Ok(())