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That's where you're wrong, this is like the hyperloop or solar roadways, where all of the experts agree it's a dumb idea but you have a rich person trying to sell that to the public with the promise that they'll solve the issues by the time they get to production.
You can't cool things in space effectively, the only way things lose heat in space is through radiation. According to Wikipedia the radiators expel from 100 to 350 W per square meter. My PC generates more heat than that, imagine a data center. A quick Google tells me it's 5-15kW per rack or 40-60kW per AI rack. Let's imagine an AI data center, a single rack produces 50kW, so you need 140 square meters per rack. To put this in perspective the space station could host one rack if we removed everything else that produces heat from inside. So you need a megastructure just to host one rack, that will become obsolete in a couple years.
It's not feasible, it's just as stupid an idea as a vacuum tube for trains, and brought to you by the same person too.
Here's the usual video I use for this issue, a walk-through of the equations on how things cool in space where Scott Manley runs the numbers and shows that it's perfectly reasonable with a modest radiator panel.
What temperature are you assuming for the radiators? At 80° Celsius (353 Kelvin) they can do 880 watts per square meter. And bear in mind that radiator panels are double-sided, so that makes 1760 watts per square meter of dedicated panel. 80 degrees is what these chips are meant to run at, if you wanted to you could use a heat pump to make the radiator panels even hotter and they'd get much more efficient - according to the Stefan–Boltzmann law thermal radiation goes up proportional to the fourth power of the temperature. Shouldn't be necessary here though.