For what felt like an eternity, advocates (present company included) would write briefs directed at Justice Kennedy, the swing vote. Erwin Chemerinsky would joke that he would put Kennedy's phot on the cover the brief, if he could. The so-called Kennedy briefs would discuss concepts such as federalism, dignity, and other related balancing tests.
After Justice Kennedy's retirement, we said goodbye to the Kennedy briefs, and advocates pivoted to the Roberts Briefs. Those filings would focus on the Court's institutional role, and preserving some semblance of the separation of powers. Alas, the Roberts Briefs had a brief shelf life. With Justice Ginsburg's passing, the Chief was no longer the fifth vote. Instead, briefs would target the other two getable votes: Justices Kavanaugh and Barrett.
At present, the most obvious Barrett briefs focus on the independent state legislature (ISL) doctrine. Consider Rick Hasen's posting on tonight's ruling from North Carolina: