Hi there,
Unfortunately, you're correct - there is currently no setting available to customize the data elements shown in the sidebar treeview.
The full-width treeview is a later addition that many of our users have favored over the display limitations of the sidebar version, and consequently more community-sponsored development effort has gone into this version than the older one. It will require additional development to add more display options to the sidebar treeview.
Not the answer you were hoping for, but I hope it helps to at least know you haven't missed something.
Cheers,