The error log, doesn't indicate a problem with storage limit - but a lot of changes to the data, that Azure Site Recovery is having difficulty keeping replicated. This could be due to the disk type selected by Azure for your virtual machine - take a look at the Metrics, as you may need to adjust the SKU of your HDD.
This document is worth a read: Azure Site Recovery limits
Also take a look at the Azure VM requirements, to make sure your servers match.
Regarding the private endpoint and your storage account - I wonder if your issue is DNS, if you do an nslookup of your endpoint, are you getting the public or private IP? Your internal DNS needs to resolve the private IP of your endpoint.