Fix async loading bugs and add test results

Critical Fixes:
- Fix async context manager usage in fastapi_app.py (async for -> async with)
- Add broadcast() method to WebSocketService
- Initialize BackgroundLoaderService properly in lifespan function

Testing:
- Execute manual testing (Tests 1, 5, 8, 9)
- Create comprehensive test results document
- Verify API endpoints return 202 Accepted
- Confirm database persistence works
- Validate startup incomplete series check

Test Results:
- Response time: 61ms (target: < 500ms) ✅
- 4 series found with missing data on startup
- Database fields properly persisted
- All critical bugs fixed

Files:
- check_db.py: Database inspection utility
- docs/MANUAL_TESTING_RESULTS.md: Comprehensive test results
- src/server/fastapi_app.py: Fixed async context manager, initialized BackgroundLoaderService
- src/server/services/websocket_service.py: Added broadcast() method

src/server/fastapi_app.py

@@ -56,7 +56,7 @@ async def _check_incomplete_series_on_startup(background_loader) -> None:
         from src.server.database.connection import get_db_session
         from src.server.database.service import AnimeSeriesService
         
-        async for db in get_db_session():
+        async with get_db_session() as db:
             try:
                 # Get all series from database
                 series_list = await AnimeSeriesService.get_all(db)
@@ -98,8 +98,6 @@ async def _check_incomplete_series_on_startup(background_loader) -> None:
             except Exception as e:
                 logger.error(f"Error checking incomplete series: {e}", exc_info=True)
             
-            break  # Exit after first iteration
-            
     except Exception as e:
         logger.error(f"Failed to check incomplete series on startup: {e}", exc_info=True)
 
@@ -218,8 +216,17 @@ async def lifespan(_application: FastAPI):
                 logger.info("Download service initialized and queue restored")
                 
                 # Initialize background loader service
-                from src.server.utils.dependencies import get_background_loader_service
-                background_loader = get_background_loader_service()
+                from src.server.services.background_loader_service import (
+                    init_background_loader_service,
+                )
+                from src.server.utils.dependencies import get_series_app
+                
+                series_app_instance = get_series_app()
+                background_loader = init_background_loader_service(
+                    websocket_service=ws_service,
+                    anime_service=anime_service,
+                    series_app=series_app_instance
+                )
                 await background_loader.start()
                 logger.info("Background loader service started")