You need to perform initialization after installation:
$ export AIRFLOW_HOME=some/dir
$ airflow db init # or `airflow initdb` for the legacy 1.X
If AIRFLOW_HOME is unset, ~/airflow/ will be created and used. This is where the config and logs will be stored; if you want to reset the configuration, remove the dir stored in AIRFLOW_HOME and rerun airflow db init.
Now other commands should work, e.g.
$ airflow db check
[2021-02-06 23:35:21,577] {db.py:756} INFO - Connection successful.
Source: Initializing Airflow Database section from airflow docs. Kudos to Anas Tiour who notified about the command line interface change in 2.0.0 in this comment!