Presently it's not possible, You can connect/mount the Azure file share into different OS system or use azcopy tool to copy the data Or Add new Recovervaullt.
This article explains how to use the Azure portal to restore an entire file share or specific files from a restore point created by Azure Backup.
Azure file share sits inside a Storage Account. Azure Backup can now see that file share and create backup snapshots of it, into the same Storage Account. To do this, the Storage Account is registered with a Recovery Services Vault, where the backup policy and retention points are managed.

Azure Backup offers a variety of options to restore your file share data. You can choose to restore the entire file share or individual files and folders. Restores can also be done to the original location or to alternate file shares in the same or different storage accounts. Azure Backup also preserves and restores all access control lists (ACLs) of files and folders.