There are only the faintest wisps of connection between the NFT and the art. It's like an autograph on the cover of a book, but without the book inside the cover. And it's not even that tangible, because the autograph is digital, and there are no limitations on infinitely and perfectly reproducing the book.
That's the benefit of owning shares, it doesn't mean you own part of the company in any meaningful way. The relationship is the same as owning an NFT instead of owning the art itself. Shares can be useful of themselves just as owning an NFT can come with some benefits like, say, a secret URL that only the owner can access.
When you buy art at auction, unless specified, or a print, you own the rights to all of it.
Its the same with a company, if you own all the shares, you can asset strip, pull apart, and generally do anything within the law to it.
unless explicitly specified in the contract of sale, the artist will retain the rights to the original work. Nothing in the NFT explicitly states that you own the original thing that you've generated the token for.
You own the art in the same way that you "own" part of a company by holding shares in it.