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.
It probably increases Elon's share of the combined entity.
It delivers on a promise to investors that he will make money for them, even as the underlying businesses are lousy.
A Starlink satellite uses about 5K Watts of solar power. It needs to dissipate around that amount (+ the sun power on it) just to operate. There are around 10K starlink satellites already in orbit, which means that the Starlink constellation is already effectively equivalent to a 50 Mega-watt (in a rough, back of the envelope feasibility way).
Isn't 50MW already by itself equivalent to the energy consumption of a typical hyperscaler cloud?
Why is starlink possible and other computations are not? Starlink is also already financially viable. Wouldn't it also become significantly cheaper as we improve our orbital launch vehicles?
The short answer is that ~100m2 of steel plate at 1400C (just below its melting point) will shed 50MW of power in black body radiation.
I would assume such a setup involves multiple stages of heat pumps to from GPU to 1400C radiatoe. Obviously that's going to impact efficiency.
Also I'm not seriously suggesting that 1400C radiators is a reasonable approach to cooling a space data centre. It's just intended to demonstrate how infeasible the idea is.