AWS Backup, backup vault to non AWS Managed S3 bucket

It is NOT possible to configure a non-AWS managed S3 bucket instead of a backup vault for S3 backups or any backups managed by AWS Backup service. There is no way to export the backup from a Backup vault. From time to time, a few customers ask for this feature to be available. Please open a support case to create a feature request for this.

Backup vaults are service managed vaults and the underlying storage is internal information. Hence, as vaults are managed by the service itself, customers do not have direct access to configure or modify the underlying storage. So, you cannot export the backups created by AWS Backup locally but if it suits your use case, you may copy the backups in another AWS account which is part of your AWS Organization. Please refer to following document for more details,

[+] Creating backup copies across AWS accounts - https://docs.aws.amazon.com/aws-backup/latest/devguide/create-cross-account-backup.html