that orbital data centers are cost-competitive compared to ground-based data centers

Might as well work off of the assumptions that magical math-faeries will do all the computing in orbit, in exchange for candy canes. It's about as realistic.

Solar irradiance is only about 25-30% more efficient in orbit, so with 40% efficiency (VERY optimistic, ISS does about 14%) a 1GW orbital datacenter would require a mere 0.4 x 10^8 / 1300 m2 worth of solar panels, or a square 550m to a side.

If we use ISS-style solar arrays, which generate ~7.5w/kg, and double the efficiency, it would weigh 66000 tons, which translates to 3800 Falcon 9 launches. Just to power it. That includes zero frames, zero GPU's, and most importantly, zero cooling.