Ok, that’s how I read what was posted.
What can happen to “unstay” the judge’s order?
The appeals court will decide whether to actually take the case. If they do, the stay will remain in place until the case is heard and a ruling made at that level or they could decide to not hear the case and the stay would be lifted (less likely because the stay being issued means they most likely will).
Depending on that ruling or lack of ruling, next step is the Supreme Court if either party appeals.