This suit was filed because no state court can overturn the order by the U.S. District court. It needs to be done by a higher Federal court.
Not really, the issue before the federal court yesterday was merely in regard to timing. The state court still has jurisdiction to rule on the recount itself and could thereby moot the decision of the federal court.
I believe the US District court order was limited to "start on Monday, instead of waiting two business days until Wednesday".
I think the two day delay was to give the state time to appeal. That appeal was made to the MI court of appeals, and the hearing is tomorrow.
If the MI court says: "no recount", it's over aside from an appeal to the MI Supreme Court.
I don't know what the grounds for the appeal to the 6th Circuit might be, unless there's more to the US District's order.