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/session/handlers.rs

@@ -49,6 +49,7 @@ use codex_protocol::protocol::TurnAbortReason;
 use codex_protocol::protocol::WarningEvent;
 use codex_protocol::request_permissions::RequestPermissionsResponse;
 use codex_protocol::request_user_input::RequestUserInputResponse;
+use codex_thread_store::PersistContext;
 
 use crate::context_manager::is_user_turn_boundary;
 use codex_protocol::dynamic_tools::DynamicToolResponse;
@@ -557,7 +558,7 @@ pub(super) async fn persist_thread_memory_mode_update(
     mode: ThreadMemoryMode,
 ) -> anyhow::Result<()> {
     let live_thread = sess.live_thread_for_persistence("update thread memory mode")?;
-    live_thread.persist().await?;
+    live_thread.persist(PersistContext::Standard).await?;
     live_thread.flush().await?;
     live_thread
         .update_memory_mode(mode, /*include_archived*/ false)