🔗 FastAPI background task queue with asyncio

When handling long-running operations—such as PDF generation, audio processing, batch notifications, or web scraping—processing them synchronously inside a FastAPI route handler blocks the response and risks timing out the client's HTTP connection.

While heavy distributed task frameworks like Celery with Redis or RabbitMQ are standard for large systems, introducing external message brokers adds significant deployment and operational overhead for small-to-medium applications. This script implements an in-memory, decoupled background task queue directly inside FastAPI using Python's native asyncio.Queue. It provides background job scheduling, task status monitoring, failure isolation, worker concurrency controls, and clean shutdown handling without relying on external dependencies.