SQL Server mirrored backup using cluster shared volumes
I hope this is Partial answer and this might helpful to you.  

Clustered Storage: clustered file system is a file system which is shared by being simultaneously mounted on multiple servers. There are several approaches to clustering, most of which do not employ a clustered file system (only direct attached storage for each node).

Local Drive Z: Microsoft says "drive", what they actually mean is a partition - a formatted block of space on an existing physical drive. In your case, the "Z" partition is most likely the EFI System Partition (ESP) which holds the boot information for the OS.

Cluster Storage and Local Drives are different from each other. 

Hardware Requirements for Backup Mirrors:

Multiple-storage servers working together to respond to multiple read and write requests. clustered file system is a file system which is shared by being simultaneously mounted on multiple servers. 

Mirroring applies both to disk and Storage file system (disks do not support continuation file system). As in earlier versions of SQL Server, all backup devices for a single backup or restore operation must be of the same type, disk or tape.

Within these broader classes, you must use similar devices that have the same properties. Insufficiently similar devices generate an error message (3212). To avoid the risk of a device mismatch, use devices that are equivalent,such as only drives with the same model number from the same manufacturer. 
or use same Cluster storage file system for Backup and Mirror paths with different folders. 

This might work:

BACKUP DATABASE [msdb] 
TO DISK = N'C:\ClusterStorage\BackupSQL\\some_path_and_name.bak' 
MIRROR 
TO DISK = N'C:\ClusterStorage\MirrorBackupSQL\some_path_and_name.bak' 
WITH CHECKSUM, COMPRESSION, FORMAT