**Apache Airflow version**:
2.0.1

**Kubernetes version (if you are using kubernetes)** (use `kubectl version`):
Not applicable

**Environment**:

- **Cloud provider or hardware configuration**: None
- **OS** (e.g. from /etc/os-release): Ubuntu
- **Kernel** (e.g. `uname -a`): 
- **Install tools**:
- **Others**:

**What happened**:

1. Ran airflow db init on mysql in parallel in 2 command lines. Only one command did the migrations, the other one waited. But connections were inserted twice. I would like them not to be added twice.
2. Ran airflow db init on postgres in parallel in 2 command lines. Both command lines started doing migrations on the same db in parallel. I would like one command to run, the other to wait.

**What you expected to happen**:

1. For MySQL. Connections and other config objects to be inserted only once.
2. For Postgres. Only one migration can be performed in the same time for the same db.

**How to reproduce it**:
Scenario 1:
Setup Airflow so that it uses MySQL.
Run `airflow init db` in 2 command lines, side by side.

Scenario 2:
Setup Airflow so that it uses Postgres.
Run `airflow init db` in 2 command lines, side by side.

**Anything else we need to know**:
This problem occurs every time.
airflow/utils/db.py
"""
    Check nullable conn_type column in Connection table
    :param session:  session of the sqlalchemy
    :rtype: str
    """
    n_nulls = []
    try:
        n_nulls = session.query(Connection).filter(Connection.conn_type.is_(None)).all()
    except (exc.OperationalError, exc.ProgrammingError, exc.InternalError):
        
        pass
    if n_nulls:
        return (
            'The conn_type column in the connection '
            'table must contain content.\n'
            'Make sure you don\'t have null '
            'in the conn_type column.\n'
            f'Null conn_type conn_id: {list(n_nulls)}'
        )
    return ''
@provide_session
def auto_migrations_available(session=None):