You can find the brief here. The Summary of Argument begins:

Petitioners’ expansive interpretation of the Elections Clause—the so-called “independent state
legislature” theory—likely will lead to a flood of new federal litigation that will further destabilize American elections and contribute to decreased public confidence both in the judiciary and in the fairness and integrity of the U.S. election system. Were Petitioners’ interpretation adopted, destabilization and loss of confidence would be inevitable as federal courts, especially this Court, would be called upon frequently to second-guess state administrative and judicial interpretation and implementation of state election laws. This
confidence crisis would emerge regardless of how carefully and competently officials run elections, state courts interpret and apply state election laws, and federal courts review those decisions of state courts and election administrators.