I don't believe this is supported currently. If you are restricting access to the storage account via a service or private endpoint then you are effectively firewalling it by denying access via the public endpoint.
It's also not possible to assign a system assigned managed identity to the Azure cost management service currently as an exception to the firewall configuration. I don't think public IP address whitelisting is a viable option either due to the fact this comes from an internal Microsoft management API service.