The physics of data centers in space will be extremely difficult and expensive to pull off in any meaningful timeline.

I fully expect "space AI" to be about as realistic as the flying cars and hover boards we've been promised since televisions were black and white.

its only a expensive to viable alternatives, is there a viable alternative for 1 terrawatt of compute on earth? how could you get approvals for such a project

The alternative would be just not building it.

I'm not sold that a data center in space is even possible unless and until we develop a drastically different solution for heat management.