Generally, the corrupt scum of Europe and Africa and the Americas focus on New York while the corrupt scum of Asia (where half the world's people live) tend to use California. I'm not sure if that's because geographical proximity matters, or if it's something else.
In addition to the purchase of safety housing by corrupt foreign officials, much bigger is the secondary market in U.S. real estate that exists because of this purchase pattern. The fact that every overseas scumbag wants a U.S. house (preferably a high-value one, because if your assets are frozen and have to change your identity, you may have to borrow against the house for 3 years while your fixers buy you a resume and get you able to work legit) in case shit goes seriously wrong, U.S. real estate has become a store of value.
I don't know the numbers. I don't think anyone does, but as for how much housing is being bought by foreign scumbags (or to sell to them, but speculators betting on scumbaggery) it's probably on the order of 1-10% on the high end, and possibly much higher (10-50%) on the ultra-high ($5M+) end. That might not seem like a big deal, but there are two things to consider. First is the push-down effect. Billionaires buying penthouses push modest millionaires into 3BRs and upper-middle-class families into 1BRs and the middle- and working classes out. It propagates down the socioeconomic chain, making everyone pay higher prices.
The second issue is extreme price inelasticity. 1% supply destruction doesn't increase prices by 1%, as one might hope or expect. It can cause them to double.