Hi Rishi,
Could you confirm you are running SQL Server on an Azure VM rather than using the Azure SQL (PaaS)? If so, it sounds like you have a security need to block internet access for the Azure VM, how are you achieving this? Depending on how you are doing this, you could create a private endpoint to the Recovery Services Vault which injects a NIC in the VNET your Azure SQL VM resides in an adjacent subnet. Depending on how/where you are blocking internet, you would allow traffic to flow from your Azure SQL VM to this subnet to reach the Recovery Services Vault to house your backups.
See: https://learn.microsoft.com/en-us/azure/backup/backup-sql-server-database-azure-vms