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/api/auth.py

@@ -163,6 +163,22 @@ async def setup_auth(req: SetupRequest):
                 # Perform NFO scan if configured
                 await perform_nfo_scan_if_needed(progress_service)
                 
+                # Start scheduler if anime_directory is now set
+                try:
+                    from src.server.services.scheduler_service import (
+                        get_scheduler_service,
+                    )
+
+                    scheduler_svc = get_scheduler_service()
+                    logger.info("Starting scheduler after initialization")
+                    await scheduler_svc.ensure_started()
+                    logger.info("Scheduler started successfully during setup")
+                except Exception as sched_exc:
+                    logger.warning(
+                        "Failed to start scheduler during setup: %s", sched_exc
+                    )
+                    # Continue — scheduler failure should not break initialization
+                
                 # Send completion event
                 from src.server.services.progress_service import ProgressType
                 await progress_service.start_progress(