If you had taken a backup of the vm, then you can restore that backup to a new azure vm using this guide:
https://video2.skills-academy.com/en-us/azure/backup/backup-azure-restore-files-from-vm
If the vm was not backed up, you can use the free GNU tool called Ddrescue to try to recover those files inside the disk.
Some of the features of ddrescue:
- Created to be fully automated
- Data is rescued very efficiently (only the needed blocks are read).
- Auto-merge data
- Automatically highlights bad sectors on a hard disk
- Backup-Recovery is resumable
Here is a full guide on how to perform that too: https://www.gnu.org/software/ddrescue/manual/ddrescue_manual.html#Examples