fix(scheduler): ensure scheduler starts after setup/config update

Add ensure_started() to SchedulerService as idempotent entry point.
Start scheduler in auth setup run_initialization() after NFO scan.
Sync anime_directory and start scheduler in config update endpoint.
Add unit and endpoint tests for ensure_started() behavior.

src/server/services/scheduler_service.py

@@ -153,6 +153,22 @@ class SchedulerService:
         self._is_running = False
         logger.info("SchedulerService stopped successfully")
 
+    async def ensure_started(self) -> None:
+        """Ensure the scheduler is running (idempotent).
+
+        If already running, returns immediately. Otherwise, starts the scheduler.
+        This method is safe to call multiple times and from multiple callers.
+
+        Raises:
+            SchedulerServiceError: If startup fails (except for already running).
+        """
+        if self._is_running:
+            logger.debug("Scheduler ensure_started called but already running")
+            return
+
+        logger.info("Scheduler ensure_started: starting scheduler")
+        await self.start()
+
     async def trigger_rescan(self) -> bool:
         """Manually trigger a library rescan.