how to backup/export office 365 email to pst in exchange hybrid environment?

You can't export Exchange Online mailbox directly to PST via PowerShell with built-in tools. Required New-MailboxExportRequest doesn't exist Online (or is not exposed to us mortals).

You can:

  • eDiscovery, that seems to be GUI-only.
  • Offload/migrate mailbox to on-prem Exchange and run New-MailboxExportRequest on-prem (and migrate back to Exchange Online if needed)
  • Use various 3rd party tools, that perform export via EWS or MAPI
  • Script delegation full access, Outlook bind to delegated mailbox and export to PST. Technically very likely possible but I've never seen anyone do it. I haven't looked deeply into eDiscovery but I believe that's more-less how eDiscovery does export to PST (Old Exchanges also used to bind to Outlook for PST export). But without significant MAPI experience, Outlook COM model is quite complex to use (I've done some Outlook scripting but emulating PST export is challenging to say the least).

I'm as frustrated as you are. Exporting mailboxes for departing users for long-term storage is needlessly annoying. If we could just export to Azure Blob just as with import, it'd be a good start.