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/tasks/user_shell.rs

@@ -39,6 +39,7 @@ use codex_protocol::protocol::ExecCommandSource;
 use codex_protocol::protocol::TurnStartedEvent;
 use codex_sandboxing::SandboxType;
 use codex_shell_command::parse_command::parse_command;
+use codex_thread_store::PersistContext;
 
 use super::SessionTask;
 use super::SessionTaskResult;
@@ -463,7 +464,9 @@ async fn persist_user_shell_output(
             .await;
         // Standalone shell turns can run before any regular user turn, so
         // explicitly materialize rollout persistence after recording output.
-        session.ensure_rollout_materialized().await;
+        session
+            .ensure_rollout_materialized(PersistContext::Standard)
+            .await;
         return;
     }