Hello @metalheart
You are right, currently it's only possible to mount Azure [Premium] File Shares in App Service. Documentation
Performance for Azure Files is Up to 100,000 IOPS(up to 80 Gib/s throughput) and Azure NetApp Files is Up to 460,000 IOPS(up to 36 Gib/s throughput).
Definitely in case of Azure NetApp Files to Azure Files migration, performance could be degraded
https://zcusa.951200.xyz/en-us/azure/storage/common/nfs-comparison
Azure AKS supports integration with Azure NetApp Files, however it would be costly and inefficient for your case.