These are solved legal problems. Cryptographic possession is a well understood legal concept that comes up all the time in contexts like custody of financial instruments or digital evidence.

> What differentiates a cryptocurrency key from a non-cryptocurrency key? Would this criminalize the holding of any private key at all, even if intended for non-cryptocurrency applications?

Intent, primarily, so no. The applicability of intent to the criminality of an action is also a well understood legal principle.

> What happens if I generate a key for non-cryptocurrency use and then someone later sends cryptocurrency to it? Am I going to jail? Do I need to rekey immediately? Is it my duty to monitor for this situation? If I'm evil, can I cause trouble by "spoiling" an enemy's known public keys in this way?

In this thought experiment with this hypothetical ban, this feels analogous to mailing cocaine to someone's house. Again, well-understood legal principles around intent cover this without issue. Based on relevant precedent for physical contraband, you'd presumably have no obligation to monitor for it, but you would have an obligation to report it if you discovered it and turn it over to authorities.

Blockchain ledger technology makes relinquishing contraband very straightforward. Once you discover that you are in possession of cryptocurrency, you can simply send it directly to a government-controlled blackhole address, and investigators will be able to trivially verify that this transaction is the only one you initiated while in possession of the cryptocurrency.

> Here's an exhaustive list of all bitcoin keys; you're now in possession of all bitcoin in circulation: https://lbc.cryptoguru.org/dio/

The legal system has been around the block on this one. The concept of criminalization of the possession of certain bit sequences when they correspond to some meaningful embedding is well understood. Child pornography is the classic example. Any arbitrary sequence of bits could in principle be child porn expressed in some highly unusual binary format, and yet somehow the legal system has successfully avoided criminalizing the possession of arbitrary random numbers. But if you happen to have a decoder for said highly unusual binary format, then you are going to jail.

Likewise if you happen to know that your "random numbers" are in fact cryptocurrency-controlling key pairs and you harbor an intent to traffic in cryptocurrencies, lo and behold, those "random numbers" suddenly transmute into a cognizable thing that can be criminalized.

Intent matters in law.