When I click on the database name/icon in the navigation area of the Items list, the icon & text shift as one might expect from a button press…but then nothing happens. Am I missing something?
(Fwiw, what I hoped would happen was for a drop-down to appear allowing me to select another database. The Navigation Sidebar was hidden at the time.)
This is the Path Bar. A breadcrumb trail that shows your location in the nested group.
You can read about the Path Bar here.
Help > Documentation > Windows > Main Window
Example:
In my Tech DB, I have the following group structure.
When I double click and go to the “architecture - planning” group , this is how it looks.
I can, then, click directly any of the ( Tech | Cloud | AWS ) to navigate in the hierarchy.
Ah. That’s actually what I’d remembered, except that I’d missed the subtlety that the breadcrumbs only appear when the root group changes.
Before posting, I’d clicked on a file (as in @hramakr’s first screenshot) and was surprised not to see the breadcrumbs updated to reflect the change. I then clicked on the database icon and was equally surprised to find it responding to clicks but not actually doing anything.
My mental model seems to have been trained by apps that keep breadcrumbs tracked to whatever’s displayed in the main content area. I appreciate your help in helping me grok DT’s idiosyncrasies here! 
And @BLUEFROG, rest assured that I’m making frequent reference to the manual (and the Take Control book). Sometimes I just can’t seem to find what I’m looking for there. 
Thanks for your patience and continued support as I try to shape my brain around DEVONThink!
Glad to hear it !
