Hi,
Backup policies are not applied to a resource group. They are applied to specific resource. From the screenshot we can see that you are searching for Azure Database for MySQL flexible server resource but you do not have such resource thus you cannot assign the policy to it. The resources that are supported by the backup vault are: Azure Disks, Azure Blobs, Azure Kubernetes (AKS), Azure Database for MySQL flexible server and Azure Database for MySQL single server. Also the resources should be located in the same region as the backup vault.
Update: Use Automated backups in Azure SQL Database where you can configure 12 hour or 24 hour frequency. You can also configure short term retention in days and long term retention in weeks, months and years.
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