Thanks for your help, and the work you've done in this beautiful and coherent presentation.
My Screenshot.app does have the Desktop as the default, but again, there is no Desktop for root user, so the screenshots seem to disappear into the ether. Try it. A "find file" cannot locate them.
I fixed the anomaly merely by adding a "Desktop" folder to the root home directory. Screenshot.app immediately started dropping screenshots into there, instead of putting them nowhere. Catalina must be fuming at me for this small expression of freedom. I'm sure she'll get back at me somehow, unfortunately.
The view option to show library is my default, but nonetheless, the root's home is an invisible path, startupVolume:private:var:root:.
el7