You don't need any major technological advances to build a proof-of-concept
You do - cooling those datacenters in space is an unsolved problem.
We have radiators on the ISS. Even if you kept the terrible performance of those ancient radiator designs (regularly exposed to sunlight, simplistic ammonia coolant, low temperature) you could just make them bigger and radiate the needed energy. Yes it would require a bit of engineering but to call it an "unsolved problem" is just exaggerating.
Sure it is, just not economically at that scale yet. But if Starship brings the cost to orbit down significantly, maybe.