fix: resolve 21 mypy type errors across backend modules

Agent-Logs-Url: https://github.com/christianlouis/InboxConverge/sessions/bc16203d-7907-4e3f-952f-18c760c85076

Co-authored-by: christianlouis <361235+christianlouis@users.noreply.github.com>

backend/app/main.py

@@ -36,7 +36,7 @@ logger = logging.getLogger(__name__)
 
 
 @asynccontextmanager
-async def lifespan(app: FastAPI) -> AsyncIterator[None]:
+async def lifespan(_app: FastAPI) -> AsyncIterator[None]:
     """Application lifespan handler for startup and shutdown events."""
     # Startup
     logger.info(f"Starting {settings.APP_NAME} v{settings.APP_VERSION}")