Ah, it’s a bug.
Here’s the demo with red squares made from thin BoxGeometries instead of PlaneGeometries, and shadow casting now somewhat works with some obvious glitchyness, and the polygon count increased by a factor of 6:
Here’s another demo more clearly showing the glitchy shadow effect when the Plane (Box) is not thick enough (line 145):
Would you consider these glitchy effects a bug?