They can, the preliminary injunction is a thing that can be invoked very quickly to stop actions before the law decides.

Anthropic didn't suffer any irreparable harm and they're free to seek damages if they wish, but they won't because it doesn't really matter to them. This whole mess has just been advertising that has kept them in the headlines and very likely has been more beneficial than harmful.

To a certain extent this exists, but given that SCOTUS has been stacked with GOPers…

> The shadow docket is a break from ordinary procedure. Such cases receive very limited briefings and are typically decided a week or less after an application is filed. The process generally results in short, unsigned rulings. In contrast, merits cases take months, include extensive briefing and public oral argument, and result in lengthy written opinions detailing the reasoning of the majority and of any concurring and dissenting justices.

* https://en.wikipedia.org/wiki/Shadow_docket