Dear Steel 6,
Welcome to Microsoft Community.
I understand that after you switched to New Outlook, Import Export turned grayed out and thus you were unable to backup your data.
The reason why Import Export is grayed out is because currently New Outlook doesn't support importing and exporting .pst files, so you can't use this feature.
When you switch back to Classic Outlook, import and export will become available.
You can click “Outlook” menu at the top left corner of the menu bar at the top of the screen in Outlook, check “Legacy Outlook” and you can go back to classic Outlook.
But they are independent software, so your mail, calendar, contacts may be different from New Outlook.
If your mailbox belongs to Microsoft domain (outlook/hotmail), your data are stored in the server.
But you may use a non-Microsoft domain mailbox, then the emails should be stored in your mail provider's server, and IMAP/POP protocol doesn't support synchronizing calendars and contacts, so your calendars and contacts may not be in your mail provider's server, you need to log in your mail provider's website to check whether the calendars and contacts exist in webmail.
If you can see them in webmail, you can synchronize them to Classic Outlook and export them as .pst file.
Feel free to post back if you need further assistance.
Best Regards,
Jason.YA - MSFT | Microsoft Community Support Specialist