Mac Time Machine + Microsoft Azure Blob Storage

Azure blob storage is less than ideal for this purpose; as others have implied you would need to store all of the file system metadata on your own.

These days, though, the "Azure Files" service does seem to be a workable option using an Azure "General purpose" storage account.

It's generally unsupported, but you should be able to use TimeMachine to back up to a SparseBundle disk image (formatted as HFS+) in the same was as with most other file shares using the SMB protocol.

See:

• Apple Time Machine Backup to Microsoft Azure (video; YouTube)
• Mount Azure file share over SMB with macOS (Microsoft)
• Creating a local drive mapped with an Azure File Share for your files in the cloud (not Mac-specific, but may have some useful information)
• Use an Azure file share with Windows (Microsoft)

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If you would like to backup to a SMB file share with macOS 10.13.3 or earlier (either locally or in the 'cloud') you'll want to read this:

• Turn off packet signing for SMB 2 and SMB 3 connections (Apple)

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Finally, if your system is so old that it doesn't support SMB version 3 (MacOS X 10.9 Mavericks or earlier), Azure Files allows the use of SMB 2.1, but only by setting up a separate VPN.

• Azure Files networking considerations (Microsoft)