tell me how I can change the background of a SketchUP view to a black background
You can’t (as far as I know)
How did you get the toolbars and trays to show white lettering on black background?
You can edit the Style to make it black.
At this time there isn’t a native option in SketchUp for making the surrounding areas black, though. You might be able to get the black for the toolbars and trays through the Windows Accessibility options. I expect the view in the OP’s screen shot was done with the inverted grayscale setting.
Styles tray, Background settings. If you want to keep black profiles and edges, make the background dark grey. With black the linework turns white.