Trust Level Permissions Table (inc Moderator Roles) suggests emails need a special setting.
There were a number of topics where people ask to reduce the exposure of email addresses.
Regardless, private messages are on profile page (click your name) using a Message button.
I’m not sure I want to go between whoever picks this up and you, though you may prefer that.
Users are always shopping for storage, and S3 is sort of a commodity on the surface, though
deeper down there are differences. I haven’t evaluated yours, but welcome to the S3-ish club.
Editing my prior post, I sort of invited you to name other things with the same limitation, which
may or may not be in your interest. It may help get the change done, while giving away ideas.
EDIT:
A PM is probably visible by the admins group but not by the moderators group (which I’m in).
Again this becomes a question of what’s “good enough” to do the data transfer well enough…