s3 backup error to aws backup

The error gives you pretty much everything you need. The role you've supplied the service doesn't have the correct permissions to complete the task. Namely it's missing events:ListRules. I would look for a guide on configuring this service as it will likely have a sample IAM role that you can use.

Reason for the error is that you don't have the correct policies in your role. I will recommend you add this AWS managed policy (AWSBackupServiceRolePolicyForS3Backup) to to the roles you intend to use to backup.

Check out "Permissions and policies for Amazon S3 backup and restore" in the documentation below for more clarification. https://docs.aws.amazon.com/aws-backup/latest/devguide/s3-backups.html