CHECKDB problem - SQL files (mdfs,ldfs etc.) in Azure Files
DBCC CHECKDB uses a Database Snapshot by default.  Database Snapshots are an NTFS feature.  When storing the database on an SMB share, they aren't available.  Try specifying the TABLOCK option for DBCC CHECKDB.

And Azure Premium Files are intended to support SQL Server database file storage.   In addition to providing shared storage for clusters, they allow you to share storage resources among SQL VMs.  Before the release of Premium Files, Azure Files was not really recommended for SQL Server database storage.

When Azure Shared Disks are GA they may provide a better option for shared storage, but currently the only two options are Storage Spaces Direct, and Azure Premium Files.