In this this hypothetical scenario though it's not even a "person" providing the funds, but a foreign government organization. A US court can't "fine or imprison" the Communist Party of China, or the Russian GRU, for example.

A US court can fine or imprison any of the individual people who comprise, direct as superiors, or act on the direction of those abstract entities that the US executive branch arranges, by whatever means (which, again, have historically included both foreign kidnapping and outright invasion) to bring before the court. Vladimir Putin is obviously, as a practical matter, much safer from that than Manuel Noriega was, but lower level individuals may not be so much.

There's always a person making the decision and moving the funds. The Russian GRU isn't a sentient entity by itself. In principle those people can be held legally accountable, although it practice it's probably impossible.