I have an Azure Storage Account with a private link associated to VNET1 / SUBNET11. Additionally I have a VM1 in VNET1 / SUBNET12. This works great - i.e. I can access the Storage Account from VM1 but not outside VNET1.
Now I peered VNET2 with VM2 in VNET2 / SUBNET21. Unfortunately I can't access the Storage Account from VM2.
What is the reason for that?
Obviously the private link set up works for VNET1. The reason why it did not work from VNET2 is that it is necessary to add an additional "Virtual Network Link" from the related Private DNS Zone to the peered virtual network (VNET2).
Establishing this link allows now resources in VNET2 to access the Private DNS Zone, what is necessary for the Storage Account access. See also https://docs.microsoft.com/en-us/azure/dns/private-dns-virtual-network-links).