Hi,
Do you have any backup available of the Microsoft Azure Backup Server's database? Without a database it will be difficult to restore anything locally.
For the backups stored in the Recovery Services Vault within Azure, you should be able to gain access to them by registering your re-installed MABS server to your existing Recovery Services Vault and then use you need to use the same passphrase that was used when backing up the workloads to Azure.
Best regards,
Leon