They already have space-based compute in terms of Starlink and Starshield. Is it much more difficult than that ?

It is much more difficult than that. Starlink is essentially IT infrastructure, which certainly produces heat but nothing on the level of pure compute. Ejecting heat in space is a difficult problem that is currently solved on the ISS with large IR radiators which take up weight and space. The size, weight, power, cost tradeoffs lean heavily in favor of ground-based compute.