Error on msdb.dbo.rds_restore_database: The provided token is malformed or otherwise invalid

Since a few days I am not able to backup / restore to / from S3 for my RDS SQL Server. When I try to restore a database from S3 I get the following error

 [2023-09-24 08:32:02.107] Aborted the task because of a task failure or a concurrent RESTORE_DB request. [2023-09-24 08:32:02.150] Task has been aborted [2023-09-24 08:32:02.153] The provided token is malformed or otherwise invalid.

In the logs I see that since 16th of September my backup jobs are failing with the same error. Since a few months nothing has changed neither in the RDS config, nor in the role. Moreover when I assume the role, I can list/read my S3 bucket.

The setup is following

1. My MSSQL RDS (Standard) and S3 are in the same account
2. The instance has option groups with SQLSERVER_BACKUP_RESTORE option
3. The role associated to it has full permissions on my backup-restore S3 bucket

Unfortunately, In the AWS UI I see that this role was not used since Sept. 15, 2023 - my last backup.

I tried to replace the role in the SQLSERVER_BACKUP_RESTORE option, used the old one and a new one, every time I get:

An error occurred (InvalidParameterValue) when calling the ModifyOptionGroup operation: IAM role ARN value is invalid or does not include the required permissions for: SQLSERVER_BACKUP_RESTORE

What are my options to make it working again, except to re-create the RDS instance?