It's a fundamental physics problem. You need to have huge radiating surfaces.
A 1GW datacenter with chips operating at 100C (which is probably doable) will need a radiator that has a surface of one square _kilometer_, and this is with all the favorable assumptions. Realistically you'll need about 2x of that.
If you want your DCs to be on a 1000km orbit (for reasonable ping times), you'll be able to _resolve_ these satellites with a naked eye!
Sorry. But this idea is fundamentally unworkable.
The current plan is for 250 kW peak with 160 m^2 radiators. It will weigh about 4 tons so you can pack 25 on one flight of Starship.
Deploy 4,000 and you're at 1 GW. That's 160 launches.
BTW: SpaceX has already manufactured and launched 10,000 Starlink satellites and Falcon 9 launches about 150 times per year. None of this seems unworkable.