At all events, your reply (1) is bullshit. This is not meant as an insult at you, but at the statute itself. After a little checking, I do see the "must have been published" language. But the relevant body is not Arxiv (your pic is unhelpful and irrelevant, now I do insult you a little bit); the relevant body for this particular question is the CMI, and their statutes. And their statutes, while obviously meant to discourage cranks, are still bullshit-a proof is a proof is a proof.

OTOH one (some person, theoretically) could establish and self-publish a proof, and THEN once its truth becomes clear to "the community", they could and would happily go through the formality of publishing in Journal X, to satisfy (bullshit) statute and later clear the road to the money. But of course people aren't interested in the problem itself for the money, it's just a nice theoretical bonus. True mathematicians are high-functioning autists who do not personally care much about money.

https://www.claymath.org/millennium-problems/rules-millennium-prizes