This headline implies a misunderstanding of what this case is actually about. This is the Thaler v. Perlmutter case. Thaler has been arguing - since 2018, before the current AI "boom" - that the copyright of a particular image that he'd generated with an AI belonged to the AI itself rather than to him.
The copyright office, and every court he's appealed to since then, have responded "AIs aren't legal persons and so cannot hold copyright." That's all this Supreme Court rejection is affirming. It's a really obvious outcome, Thaler is basically a loon with too much money and time on his hands for continuing to pursue the case.
It doesn't address the general copyrightability of AI-generated art. In this particular case Thaler is explicitly saying "I don't hold the copyright, my AI holds the copyright." The courts have said "well, if you don't hold the copyright and the AI can't hold the copyright, that means nobody holds the copyright and therefore this particular piece is in the public domain." Thaler is allowed to disclaim his own copyright over the work, he just can't assign it to an AI like this.