The Right-click Context Menu that appears when the search box does not have focus is clearly the main Explorer window System Menu which is normally accessible via ALT+SPACE. When the Search Box does have keyboard input focus, a right-click does not produce a context menu at all!
Please explain?
Yep, this is a bug as seen here https://twitter.com/WithinRafael/status/1222250069472108544. You'll have to give the fake textbox focus (via keyboard or left-click) before it will show the context menu.
I'll file bugs and try to push the Shell team to fix it, but I'll need your help! File bugs in Feedback Hub, tweet @WindowsInsider @jenmsft @brandonleblanc, keep making noise here, etc.