What is an NFT from an artist’s perspective?

Proof of authenticity, whether being digital or not, doesn't mean anything until

1) the culture of the general people around you support it, or

2) there is an entity with political power (such as the state) that forcefully protects that authenticity through law/police/the military/etc (for example, intellectual property supported by law enforcement).

But firstly I think NFTs are totally antitheical to the current culture of the Internet era, where it is given without question that data can be freely copied and shared (regardless of the countless efforts by DRM technologies), and virality and mass transmission is regarded as an important communal cultural value. Who cares if someone "owns" the Nyan Cat meme, when you can freely Google it and view it on your smartphone, and can also save it to your hard drive if you want to preserve it? And I really don't think state power is really supportive of general crypto right now, so number two is off from the start. The problem I have with NFTs (and cryptocurrenties in general) isn't about the technology, it's more about the culture surrounding it.

(Also, think the blockchain is permanent, because it's supported by "math"? If the infrastructure surrounding Ethereum vanishes, your piece of NFT is essentially gone. And Ethereum's consuming a hell of a lot of energy and infrastructure to maintain, and you might start to think backing it up in a few hard drives is the easier and saner option...)

Do you have a system in place for an artist to say “hey some asshole registered my art before I even heard of your project, no seriously, here is a screen grab of it in the editor/a closeup of the canvas/some other snippet of the Original File”?

You can't restrict ownership of physical goods or art really, it's just that there's "authentic" goods and "fake" goods.

So you're right you can't restrict possession of digital goods but you can restrict the right to sell a digital good because any potential buyers will want to know what they're buying is "authentic".

CSGO skins go for thousands with the rarest going for tens of thousands, you can download them and possess them right now but valve says you don't "own" them and can't sell them.

The fatal problem is literally: "who cares". Real "authenticity" doesn't comes from math and comes instead from culture. Using the "if a tree falls in a forest" philosophy meme: if the blockchain claims that you have the Nyan Cat image but nobody cares about it, then do you really "own" the image?

More about the history of authenticity: Religion supplied this culture of "authenticity" for some time, but after the Industrial revolution the widespread duplicate production of commodities, along with the invention of photos and videos, has been eroding away the value of the authentic "the one and only" irrelevant for some time. Walter Benjamin has a nice essay about this change of culture in his famous essay - " The Work of Art in the Age of Mechanical Reproduction". And the Internet seems to further accelerate the notion of communal art, where memes only have value if they are shared freely and not when someone hangs it in a museum. My gripe with NFTs has nothing to do with the technicalities of crypto and everything to do with everything else (primarily, politics and culture in relation to technology).