Aurora Postgres DB Cluster can't access S3 for copying data via s3_copy

Postgres DB engine: 14.10

After much experiment, I found out that Aurora Postgres Cluster can not access S3 for copying data. For otherwise exactly same setup, a native RDS Postgres instance can access s3 for copying data. I followed this article on setting up the environment: https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_PostgreSQL.S3Import.html

I have a Aurora postgres cluster - playground-1-cluster and a postgres (not Aurora) - test-db-1-s3-copy

In the end, I found postgres (not Aurora) - test-db-1-s3-copy is able to access S3 and copied the data. But Aurora postgres cluster - playground-1-cluster is met with error: "SQL Error [XX000]: ERROR: Unable to generate pre-signed url, look at engine log for details."

Here are the summary steps:

1. IAM Role Permissions - role -rds-s3-import-role has the necessary permissions to access the S3 bucket. The role has policy attached - s3:GetObject, s3:ListBucket,  on the relevant S3 bucket and bucket/*
2. Trust Relationship. The IAM role has a trust relationship with the RDS service to assume the role.
3. Attached the role to the RDS, so it can assume the role.

• The role is added to the DB cluster for Aurora-Postgres. It is not possible to add to a write instance directly in the cluster

aws rds add-role-to-db-cluster \
   --feature-name s3Import \
   --db-cluster-identifier arn:aws:rds:eu-west-1:1234567890:cluster:playground-1-cluster \
   --role-arn arn:aws:iam::1234567890:role/rds-s3-import-role \
   --region eu-west-1

- It is not possible add the role to the instance direct for **Aurora-Postgres**
aws rds add-role-to-db-instance \
   --db-instance-identifier playground-1\
   --feature-name s3Import \
   --role-arn arn:aws:iam::1234567890:role/rds-s3-import-role \
   --region eu-west-1

An error occurred (InvalidDBInstanceState) when calling the AddRoleToDBInstance operation: The playground-1 DB instance is associated with a database cluster. Manage the arn:aws:iam::1234567890:role/rds-s3-import-role IAM role from the cluster instead of from the DB instance.

• Or added to the db instance directly for RDS Postgres

aws rds add-role-to-db-instance \
   --db-instance-identifier test-db-1-s3-copy \
   --feature-name s3Import \
   --role-arn arn:aws:iam::1234567890:role/rds-s3-import-role \
   --region eu-west-1

4. Check S3 Bucket Policy is not blocking the access from this role.
5. VPC Endpoint for S3 to allow private data subnets access. This is not mentioned in the article, but is needed.
6. Create aws_s3 extension and its dependencies on the db instance.

It looks to me that the problem is we can't attach the role rds-s3-import-role to a db instance in Aurora cluster, which is required for access S3. Please advice. Thanks