I thought all they did was decide whether there was a legal error or not. In general.
In general you are right, the State Supreme Court mainly decides appeals, though it does have original jurisdiction over some state-related issues and therefore can sometimes act as a trial court. And sometimes State Supreme Court judges can serve pro tem (temporarily) in a Superior court--but in that case, they would be effectively a Superior Court judge, not a Supreme Court judge. Keep in mind also that a Supreme Court's decision on appeal of a lower court's ruling can have the practical effect of "deciding" whether or not someone is competent, because the lower court's ruling is either affirmed, or reversed without any remand allowing the lower court to re-consider the issue.
No attorney-client or confidential relationship is created through this communication. Answers to questions are for educational purposes only. I only have the facts you gave me, and without a more complete consultation there could be other facts I don't know that could change what legal principles apply. Your issue may be time sensitive and may result in loss of rights if you do not obtain an attorney immediately.
Years licensed, work experience, education
Peer endorsements, associations, awards
Publications, speaking engagements