Unable to start Airflow worker/flower and need clarification on Airflow architecture to confirm that the installation is correct

The ImportError: No module named postgresql error is due to the invalid prefix used in your celery_result_backend. When using a database as a Celery backend, the connection URL must be prefixed with db+. See https://docs.celeryproject.org/en/stable/userguide/configuration.html#conf-database-result-backend

So replace:

celery_result_backend = postgresql+psycopg2://username:[email protected]:5432/airflow

with something like:

celery_result_backend = db+postgresql://username:[email protected]:5432/airflow

You need to ensure to install Celery Flower. That is, pip install flower.