Because the sun hides at night. Scientists have yet to figure out where he goes. Until that happens it’s not a great power source.

Overprovision solar and add batteries for the night, then. Whatever amount of money and effort is required to make space data centers feasible (launching, cooling, etc) cannot possibly be lower than just building solar powered terrestrial data centers + batteries or alternative power sources. It is just not as sexy a story to sell to investors as magic space computers.

What do the satellites do in earth's shadow?

Polar orbit. We’re already doing this.

What do they do in earth's shadow in a polar orbit?

Avoid it as much as possible. They'll circle the earth around an axis approximately in line with the earth-sun vector. In practice they might see some eclipse, but only for a small percentage of their orbit.

What do they do during that eclipse?

Sleep.