A lot of these is a supercomputing Dyson swarm.
Also do chips in space need casing or could the wafers be just exposed on that back layer?
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!