But what would happen if a state wants to attack Bitcoin and uses a vast amount of compute budget (in the billions). What would happen?

Here's a list of what I predict will happen (with no particular order):

Billions of tax payer's dollars would be wasted. The Bitcoin network would continue operating, as the state cannot endlessly retain this attack, because it doesn't have the money.
People would likely consider Bitcoin transactions prone to reversal for quite a lot of time.
If this happens in the far future, then perhaps the government that attempted to do it will be sanctioned by other governments that save / invest in Bitcoin.
Some people will take advantage of their transactions being unconfirmed and double-spend them.

Here's a list of the reasons I think this is unlikely to ever happen:

It'd require an astonishingly efficient coordination between the government people. And usually, they don't work efficiently, because... they're bureaucrats.
It'd require vast amounts of money such that they'd be more incentivized to issue and earn the number #1 asset in the world, than destroy it.
They would have to purchase an unusually large number of ASICs, and setup a noticeably long infrastructure. I don't believe there even exist so many ASICs, so they'd probably have to manufacture their own.

Did I mention that bureaucrats do not work efficiently?

They'd have to spend insane amounts of electricity (inb4 energy shortages) to... prove their point. Would Greta approve that?