I don't think the case was reviewed by the Supreme Court, they rejected it not on the merits, they rejected because they want a case in dispute. Meaning this paricular federal Circuit/District in Indiana ruled om favor of the vaccine mandate. USSC is waiting for another Circuit to rule otherwise. At that point in time the USSC will determine which side is right.
That is not how it works. This is: A case is filed in federal district court. If the plaintiff loses, he can appeal to a federal appellate court in the appropriate circuit. If the defendant loses, he can do the same. the case will be heard by an appellate panel, usually composed of three judges. (A loser in appellate court can ask for another hearing by all the judges, but that's rare.)
Whoever loses can try to appeal to the Supreme Court. But the Supremes reject most of the writs of certiorari that come before them. They only choose to hear those that raise the most important issues. And they must be constitutional questions.