Refactor scheduler lock implementation with heartbeat mechanism

- Add heartbeat-based lock renewal in scheduler_lock_heartbeat.py
- Update scheduler_lock.py with improved lock management
- Add comprehensive tests for scheduler lock functionality
- Update deployment and task documentation

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/app/utils/scheduler_lock.py

@@ -51,11 +51,16 @@ log: structlog.stdlib.BoundLogger = structlog.get_logger()
 
 # Lock record expires if heartbeat hasn't been updated for this many seconds.
 # This prevents stale locks from a crashed instance from blocking new startups.
+# Set conservatively to allow temporary delays (e.g., high load) before considering
+# the lock abandoned.
 SCHEDULER_LOCK_TTL_SECONDS: int = 60
 
 # Heartbeat interval: how often to update the lock's heartbeat_at timestamp.
-# Must be less than TTL to prevent premature expiration.
-SCHEDULER_LOCK_HEARTBEAT_INTERVAL_SECONDS: int = 10
+# Must be significantly less than TTL (at least 3-4x smaller) to allow multiple
+# consecutive missed heartbeats before the lock is considered stale.
+# With TTL=60s and interval=5s, the lock survives ~12 missed heartbeats before
+# expiring, providing robust protection against temporary delays.
+SCHEDULER_LOCK_HEARTBEAT_INTERVAL_SECONDS: int = 5
 
 
 async def init_scheduler_lock_table(db: aiosqlite.Connection) -> None: