It takes no justices for a filing to be made. They don’t make filings to themselves.
The Rule of 4 is whether or not they will hear an appeal. There is no “vote” on such a matter.
I don’t think this is an appeal but a filing for the Court to hear a case in Original Jurisdiction.
Actually it takes 4 justices to agree to review the case. I believe they review cases normally on Wednesday. That’s where they decide whether or not to hear a case. I had read that they had already decided to hear the case. Apparently that is not correct. However I doubt the court will refuse to hear a state vs state case as they are the only court of relief for a state.