Why does my environment texture show up in Eevee but not Cycles? In the first image, I'm using Eevee with an environment texture -- the star field background is clearly visible.  But, if I change nothing but the rendering engine (to Cycles), the environment disappears.

This is 2.80 beta (2019-01-07).  I get the same result on Windows and Mac, with multiple recent 2.8 beta builds.
I found my own answer with endless setting-tweaking:  in the Render settings, the Film > Transparency checkbox was selected.  The tooltip says "World background is transparent, for compositing render over another background."

Serves me right for being a beginner.