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/local/mod.rs

@@ -54,6 +54,7 @@ use crate::ListThreadsParams;
 use crate::ListTurnsParams;
 use crate::LoadThreadHistoryParams;
 use crate::MoveThreadToSectionParams;
+use crate::PersistContext;
 use crate::PrepareForkParams;
 use crate::PreparedFork;
 use crate::ReadThreadByRolloutPathParams;
@@ -400,7 +401,11 @@ impl ThreadStore for LocalThreadStore {
         Box::pin(async move { live_writer::append_items(self, params).await })
     }
 
-    fn persist_thread(&self, thread_id: ThreadId) -> ThreadStoreFuture<'_, ()> {
+    fn persist_thread(
+        &self,
+        thread_id: ThreadId,
+        _context: PersistContext,
+    ) -> ThreadStoreFuture<'_, ()> {
         Box::pin(async move { live_writer::persist_thread(self, thread_id).await })
     }
 
@@ -615,7 +620,7 @@ mod tests {
             .await
             .expect("append live item");
         store
-            .persist_thread(thread_id)
+            .persist_thread(thread_id, PersistContext::Standard)
             .await
             .expect("persist live thread");
         store
@@ -843,7 +848,10 @@ mod tests {
         )
         .await
         .expect("create live thread with inherited context");
-        live_thread.persist().await.expect("persist thread");
+        live_thread
+            .persist(PersistContext::Standard)
+            .await
+            .expect("persist thread");
         let inherited_metadata = runtime
             .get_thread(thread_id)
             .await
@@ -1277,7 +1285,7 @@ mod tests {
             .await
             .expect("append initial item");
         first_store
-            .persist_thread(thread_id)
+            .persist_thread(thread_id, PersistContext::Standard)
             .await
             .expect("persist initial thread");
         first_store
@@ -1337,7 +1345,7 @@ mod tests {
                 .await
                 .expect("create live thread");
             primary
-                .persist_thread(thread_id)
+                .persist_thread(thread_id, PersistContext::Standard)
                 .await
                 .expect("persist thread for resume");
             let rollout_path = primary