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
Azure AKS supports integration with Azure NetApp Files, however it would be costly and inefficient for your case.