Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build a heat exchanger. You can't exchange heat with vacuum. You can only radiate heat into it.
Heat is going to limit the compute that can be done in a satellite data centre and radiative cooling solutions are going to massively increase weight. It makes far more sense to build data centers in the arctic.
Musk is up to something here. This could be another hyperloop (i.e. A distracting promise meant to sabotage competition). It could be a legal dodge. It could be a power grab. What it will not be is a useful source of computing power. Anyone who takes this venture seriously is probably going to be burned.
Note that KSP is a game that fictionalizes a lot of things, and sizes of solar panels and radiators are one of those things.
To be clear I’m not advocating KSP as a reality simulator, or that data centers in space isn’t totally bonkers. However the reality is the hotter the radiator the smaller the surface area for pure radiance dissipation of heat.
Can you point to a terrestrial system similar to what you are proposing? Liquid cooling and phase change cooling in computers always has a radiator that is cooler than the component it is chilling.
You can do this in theory, but it takes so much power you are better off with some heat pumping to much bigger passive radiators that are cooler than your silicon (like everything else in space).