I’d thought something like this is a FAQ but the database docs on postgres don’t write a bit about forcing Django to connect using SSL to the database server.

After lots of googling (and finding hundreds of guides how to set up a Django with HTTPS) and finding out by try-and-error, behold the solution:

DATABASES = {
    'default': {
        'ENGINE': 'django.db.backends.postgresql_psycopg2',
        'NAME': 'dbname',
        'USER': 'dbuser',
        'PASSWORD': 'dbpassword',
        'HOST': 'dbhost',
        'OPTIONS': {
            'sslmode': 'require',
        },
    },
}