CREATE EXTENSION using cloud_sql_proxy fails due to insufficient privileges - django

Question

My goal is to enable the ltree postgres extension in an automated way (GCP PostgreSQL extensions).
This is the query needed to create the extension
CREATE EXTENSION IF NOT EXISTS ltree;. I verified that this command works when I manually connect to the cloudsql instance using the following method. When I do this, the migrations run fine for that instance.
gcloud sql connect MyBackendInstance --user=postgres
postgres=> \c my_database;
Password:
SSL connection (protocol: TLSv1.3, cipher: TLS_AES_256_GCM_SHA384, bits: 256, compression: off)
You are now connected to database "my_database" as user "postgres".
mch_staging=> CREATE EXTENSION IF NOT EXISTS ltree;
CREATE EXTENSION
Now I have the following django migration from a library called django-ltree, which works perfect on my local installation.
migrations.RunSQL(
"CREATE EXTENSION IF NOT EXISTS ltree;",
"DROP EXTENSION ltree;"
)
However, when I run that migration in my pipeline (without manually installing the ltree connection using the method above), which uses the cloud_sql_proxy to connect to the database, I get the following error:
Traceback (most recent call last):
File "/usr/local/lib/python3.7/site-packages/django/db/backends/utils.py", line 82, in _execute
return self.cursor.execute(sql)
psycopg2.errors.InsufficientPrivilege: permission denied to create extension "ltree"
HINT: Must be superuser to create this extension.
The command in the pipeline is quite simple:
./cloud_sql_proxy -instances="$CLOUD_SQL_INSTANCES"=tcp:5432 -credential_file=gcloud-api-credentials.json &
python backend/manage.py migrate
The credentials to connect with the database are correctly defined in the django settings, we've been able to use these credentials to perform all kinds of migrations for ages.
I have tried creating a new user as described in this question, this did not solve the issue and thus seems unrelated.
UPDATE I tried running the cloud_sql_proxy locally, using the same authentication file to install a different extension, and that seems to work flawlessly.