What

Add `GUARDED_BY(_mutex)` to the member field in `BackgroundSync` accessed without the mutex at line 896. Add `REQUIRES(_mutex)` to the private helper that reads it.

Files: `bgsync.cpp` (line 896).

Resolves: SERVER-109534

Why

Background sync state is shared between the sync thread and control threads. Because Coverity cannot be run locally, `GUARDED_BY` is the most reliable way to confirm the fix is correct and to prevent this field from being accessed without the lock in the future.