I understand that the multi-layer insulation idea doesn't accomplish much unless you're trying to reach deep cryogenic temperatures passively (as infrared telescopes do!) It's a difficult structural design which would only cut your heat budget by a small constant factor. Remember that much of that heat on the solar side is making its way over to the cold side by way of electricity—the compute units are a heat "source" of similar magnitude as the solar input itself.

edit: I think the optimal packing could be a simple rolled-up scroll, that unfurls in space into a ribbon. A very lazy design where the ribbon has no orientation control, randomly furls and knots; and only half of it is (randomly) facing the sun at any given time. And the compute units are designed work under those conditions—as they are to be robust against peers randomly disappearing to micrometeorites, to space radiation, and so forth.

Because, you could make up for everything in quantity. A small 3x5 meter cylinder of rolled-up foil stores—at the mm-thickness scale, 10's of gigawatts of compute; at the micron scale, 10's of terawatts. Of course that end is far-future sci-fi stuff!

> Also do chips in space need casing or could the wafers be just exposed on that back layer?

Even in LEO they benefit tremendously from radiation shielding, even a couple millimeters of aluminum greatly reduces the total ionizing dose. Also LEO has the issue of monatomic oxygen in the thermosphere which tends to react aggressively with the surface of anything it touches. An aluminium spacecraft structure isn't really affected, but I don't think it'd be very good for a semiconductor wafer.