Interestingly NASA had an idea of a plan that sounds at least technically possible, but it's a multi-decade operation and doesn't look anything like what the current startups are pitching. Of course you can have your data centers in space, why the fuck not, but a data center sits on top of a lot of boring old infrastructure which nobody's excited to talk about.
It's going to be prohibitive if you have to pay the gravity tax every time you want to move 1 ton of metal, so realistically this kind of high-tech project cannot even begin without having substantially industrialized the moon. Nothing fancy but you'll need at least some mining and refining, and solid trans-lunar logistics routes. Probably some housing for a bit of personnel too. At that point the space data center would be dwarfed by the size of its own support system.