There really are NO appellate options for the state at this point. They can ask for the same panel to reverse itself (most unlikely) or they can ask for a hearing En Banc (where the judges of the entire Sixth Circuit form a panel to review the case). There is NO appeal of anything to the United States Supreme Court. There are merely petitions to be heard (more commonly known as petitions for Writs of Certiorari). The Sup. Ct. gets a little fewer than 20,000 such petitions a year. The Sup. Ct. grants less than 100.
Nothing is likely to happen in Michigan until a new decision is rendered below (in the court where the matter originated). That is the present disposition of the case. The Sixth Circuit has made its ruling. And unless that ruling is disturbed in accordance with the deadlines, and also consequent to a revised ruling of the panel or a new ruling of the full bench, the case goes right back where it started. Only, now, the lower court MUST render a final order that is in line with the Sixth Circuit’s opinion. And, yes, any new order from below may be appealed back to the Sixth if either side feels that the judge has misapplied the Circuit court’s holding either as a matter of law or as applied to whatever facts are before the court.