Hi Beth, I know there have been a couple of bugs related to draft editing and approvals since 2.3.5.3 (like this and this), but I think they have all been addressed as of 2.3.7.5. I just took a look at our development site, which is built from source as of a few days ago. and as Administrator I'm seeing all of the draft approval icons, between the "settings" and "edit" icons (when viewing the instance on the page). You are Administrator, not Content Administrator, right?
I did just notice that when you're in the editor view, the only options at the bottom are Update Draft (button) Compare Draft to Live (link) and Cancel (link). Did there used to be submit for approval/approve buttons or links there in the past? I can't remember if that's how it used to work.
Jamie