xAI is now (or will very soon be) part of SpaceX.

They physically own massive 'Colossus' datacenters with tons of GPUs.

As to leasing vs owning, I already addressed that.

If you are the government and you are half of the shareholders, you can pressure your own AI company, or the companies from whom your AI company leases GPUs from to be more honest and transparent regarding accounting methodologies.

Bernie is not proposing that any taxpayer money be put toward this at all.

The only actual expense here would be the minute cost of simply hiring some people to run and manage the sovereign wealth fund. Miniscule in comparison to the potential equity value of $$$s being managed. Think something like the administrative cost of running say, the SEC or FTC, in comparison to the amount of money moving around that they can affect.

He is proposing the government simply half nationalize these companies, as Trump not long ago did with TikTok.

If the government is half of every US based AI company's board, they can also very effectively pressure them to make the models open source.

Not sure if you don't understand the concept of nationalization, but basically, thats when the government looks at something and says 'i own this now, because I say so'.

Theres no payment. Its... why I use the word 'seize'.

Same way Marx argued that workers should 'seize' the means of production: Just take them.