bash script for aurora psql db backup snapshots and export to S3 bucket

You can use EventBridge to schedule a lambda, then use boto3 to take the snapshot directly to S3, like this example to star/stop the instance, just change the stop_db_cluster for create_db_snapshot, like this example:

rds_client.create_db_snapshot(DBSnapshotIdentifier=snapshot_id, DBInstanceIdentifier=instance_id)

Then create a S3 lifecycle policy to expire the files.