> A foreign bank can hold USD without any US oversight
If they hold it as hard cash, practically, sure. If they want to be allowed to send or receive wires and generally not get sanctioned by the United States, no. The U.S. Treasury claims international jurisdiction over U.S. dollars [1].
Definitely have suprising powers. I once sent a wire payment in USD from my Hong Kong company’s HSBC business bank account directly to my China company’s bank inside China, where my bank in China would convert it to renminbi. I was shocked to find out the bank wire was somehow held up in NYC! Blew my mind. Nothing to do with the USA in this transaction, except the USD. The reason the wire was held up? I had wrote the word “Grenade” in the notes field of the bank wire. The payment was a materials deposit for an action camera mount product we make at my factory called “Grenade Grip”. I regularly write the product name in the notes field for my accountants. Mistake.
There is no such thing as a non-US bank holding electronic USD. All non-US banks hold USD via a US “correspondent bank”, and a USD transfer from one non-US bank to another amounts to the sender telling their correspondent US bank to transfer to the other bank’s correspondent (US) bank, and credit the account of the receiver.