On May 25, the New Jersey Secretary of State told the U.S. Supreme Court that she does not intend to respond to the cert petition filed in Mazo v Way, 22-1033. Of course if the Court asks for a response later, she will respond.
Two more amici on the side of the candidates who brought the lawsuit were filed on May 25. Here is the brief of Michael D. Byrne, a New Jersey Republican official.
Here is the brief of four New Jersey law professors, also on the side of the candidates.