The Supreme Court is an appellate court and these days has almost complete discretion as to what appeals it will hear.
However, Article III of the Constitution gives the Court original jurisdiction to hear lawsuits by one State against another State. The Supreme Court becomes the trial court and obviously there is no appeal from its decisions.
In the last century those have mostly been water rights cases where one State sues another claiming the other State is taking too much water and is depriving the other State of its property. Colorado has been sued by some downstream States.
The Supreme Court in those cases does not actually conduct a trial. The trial is usually delegated to an appointed Special Master who conducts pretrial proceedings and a trial if necessary. The Supremes then base their decision on that record.
I don't know how Texas proposed the Supremes should have proceeded if they had accepted this case.
The Alito/Thomas dissent was as to a technical procedural issue. They contend the Court does not have discretion to decline to accept a case filed as an original jurisdiction case. As a practical matter that would mean the case is filed and docketed, but the Defendant States would then file Motions to Dismiss which would be briefed and then decided by the Court. It wouldn't have made a difference in this case since at least seven Justices believed that Texas did not have standing and would have voted to dismiss the case.
Thanks, but I still don’t understand the time.