This seems pretty complicated. The argument the Supreme Court seems to be making is that because the 5th Circuit court's order was an "administrative stay" rather than a "stay pending appeal", the judgment of the court shouldn't be questioned, since an administrative stay is supposed to be a very temporary thing not normally subject to legal tests and requirements because the point is to be a tool for court procedure and they don't want to mess with that:
But such orders rarely generate opinions, which means that there is no jurisprudence of administrative stays, much less a one-size-fits-all test that courts apply be- fore entering one. That does not strike me as a problem: Play in the joints seems appropriate for a measure that functions as a flexible, short-term tool.
So far as I know, this Court has never reviewed the decision of a court of appeals to enter—or not enter—an administrative stay. I would not get into the business. When entered, an administrative stay is supposed to be a short-lived prelude to the main event: a ruling on the motion for a stay pending appeal. I think it unwise to invite emergency litigation in this Court about whether a court of appeals abused its discretion at this preliminary step—for example, by misjudging whether an administrative stay is the best way to minimize harm while the court deliberates.
https://www.supremecourt.gov/opinions/23pdf/23a814_febh.pdf#page=16
From what the article is saying, it sounds like the law is currently blocked again because the 5th Circuit changed their mind or something?
The 5th Circuit panel, in a 2-1 vote, lifted the administrative stay ahead of arguments on whether to once again put on hold the lower-court injunction while Texas pursues an appeal.