On June 1, the Ohio groups trying to get an initiative on the ballot asked the U.S. Supreme Court to reinstate the ruling of the U.S. District Court that had granted relief, and to lift the stay the Sixth Circuit had imposed on that relief. Thompson v DeWine. There is no case number yet. Here is the Supreme Court filing.
This is the first ballot access case involving the health crisis that has reached the U.S. Supreme Court. In the meantime, the request for Sixth Circuit rehearing is still pending.