Every organization has a unique identifier in our system, so backup from one organization can't be moved directly to another. To do so, the tenant and its data have to be purged from the initial organization and then activated on the other organization, which would be a new backup.
Once purging is done, the previously backed-up data can't be recovered from the old organization. If old data from the initial organization is required, it can be recovered using features such as restore, migrate, or download before purging.
To back up the domain's SharePoint, Groups, and Teams under a new organization, we would have to delete the existing backup from the old organization. After deletion, the previously backed-up data is purged and can't be recovered from the old organization. Once this is done, the SharePoint, Groups, and Teams backup will start on the new organization.