That was an appeal from a Temporary Restraining Order, not a final decision. Steiner could seek an emergency stay order, but she would have to allege that the District Court abused its discretion in doing something that the prior decision of the Court of Appeals told him to do.
See, there is a way to get back in front of the 6th Circuit!
I don't think there's much point in getting into the technical weeds, but I think she has at least one other failed argument she could deploy.
The context remains in the nature of TRO, she should have one and the District Court erred in denying it.
And as you note, the 6th Circuit can use FRAP to kick her out, if they want to. If she does appeal, I think they'll boot her on substance, not procedure.