As the other poster mentioned, DBT is an open core product and I'm not sure how you'd use the cloud service on a local DB install anyway. Airflow and DBT don't really do the same things anyway.
DBT is open source and can be used entirely for free. They sell a hosted version.
Also DBT and Airflow are different tools, aimed at solving completely different problems. The Airflow competitor in this article is Dagster, which is also open source.