How to properly set up custom User model and multiple databases with Django?

I created a custom application to authenticate users and have hard times to make everything work with multiple databases.

Basically, I create multiple Django projects and want a unique database for authentication and a custom AUTH_USER_MODEL. The databases are declared in settings.py with two routers, one for the auth, contenttypes, and authentication application, and the other router for the rest of the applications.

I successfuly migrated the custom User model and created createsuperuser with the option --database=auth_db but then, when I work in the admin section an create an object in one of my applications Django throws an error :

IntegrityError at /admin/django_celery_beat/crontabschedule/add/
insert or update on table "django_admin_log" violates foreign key constraint "django_admin_log_user_id_c564eba6_fk_authentication_user_id"
DETAIL:  Key (user_id)=(1) is not present in table "authentication_user".

As you can see, it says the user with ID 1 isn’t created, but I’m logged with it and I’m 100% sure the custom User model was created in the authentication app:

root@ec00652b9b9a:/app# python manage.py migrate authentication --database=auth_db
Operations to perform:
  Apply all migrations: authentication
Running migrations:
  Applying contenttypes.0001_initial... OK
  Applying auth.0001_initial... OK
  Applying authentication.0001_initial... OK

root@ec00652b9b9a:/app# python manage.py migrate contenttypes --database=auth_db
Operations to perform:
  Apply all migrations: contenttypes
Running migrations:
  No migrations to apply.

root@ec00652b9b9a:/app# python manage.py migrate auth --database=auth_db
Operations to perform:
  Apply all migrations: auth
Running migrations:
  No migrations to apply.

root@ec00652b9b9a:/app# python manage.py migrate admin --database=default
Operations to perform:
  Apply all migrations: admin
Running migrations:
  Applying admin.0001_initial... OK

root@ec00652b9b9a:/app# python manage.py migrate sessions --database=default
Operations to perform:
  Apply all migrations: sessions
Running migrations:
  Applying sessions.0001_initial... OK

Does it means Celery beat or admin is looking in the wrong database ? How could I investigate the issue further more ?

databases_router.py

class AuthRouter:
    route_app_labels = {'auth', 'contenttypes', 'authentication'}

    def db_for_write(self, model, **hints):
        if model._meta.app_label in self.route_app_labels:
            return 'auth_db'
        return None

    def db_for_read(self, model, **hints):
        if model._meta.app_label in self.route_app_labels:
            return 'auth_db'
        return None

    def allow_relation(self, obj1, obj2, **hints):
        if (
            obj1._meta.app_label in self.route_app_labels or
            obj2._meta.app_label in self.route_app_labels
        ):
            return True
        return None

    def allow_migrate(self, db, app_label, model_name=None, **hints):
        if app_label in self.route_app_labels:
            return db == 'auth_db'
        return None


class AppsRouter:

    def db_for_write(self, model, **hints):
        return 'default'

    def db_for_read(self, model, **hints):
        return 'default'

    def allow_relation(self, obj1, obj2, **hints):
        return True

    def allow_migrate(self, db, app_label, model_name=None, **hints):
        return True

settings.py

DATABASES = {
    'default': {
        'ENGINE': 'django.db.backends.postgresql',
        'NAME': env("PROJECT_DB_NAME"),
        'HOST': env("PROJECT_DB_HOST"),
        'PORT': env("PROJECT_DB_PORT"),
        'USER': env("PROJECT_DB_USER"),
        'PASSWORD': env("PROJECT_DB_PASSWORD"),
        'OPTIONS': {'sslmode': 'require',
                    'options': '-c search_path=public'
                    },
    },
    'auth_db': {
        'ENGINE': 'django.db.backends.postgresql',
        'NAME': env("AUTHENTICATION_DB_NAME"),
        'HOST': env("AUTHENTICATION_DB_HOST"),
        'USER': env("AUTHENTICATION_DB_USER"),
        'PORT': env("AUTHENTICATION_DB_PORT"),
        'PASSWORD': env("AUTHENTICATION_DB_PASSWORD"),
        'OPTIONS': {'sslmode': 'require',
                    'options': '-c search_path=public'
                    },
    },
}

DATABASE_ROUTERS = ['project.databases_router.AuthRouter', 'project.databases_router.AppsRouter']

AUTH_USER_MODEL = 'authentication.User'