You might need to check with your administrator (or if you yourself are managing it, you need to log in with admin account), there is a option somewhere there at admin.google.com to let your users export data.
Thanks for the tip. Unfortunately, I searched the settings and can't find anything that seems related that isn't already set to ON. I'm the only user (Super Admin).
This KB article might help: https://support.google.com/a/answer/6396995?hl=en
> You have no services enabled for which data can be exported.
What? I've had this (paid) GSuite account for years. That's a bit discouraging.