Mark, I'm no historian, so I can't really confirm if "aparelhamento" derives from the communist cells "aparelhos" that were persecuted by the Brazilian military government. But I can say that "aparelhamento" and "partidarização" are similar, but not quite the same, IMO. To me, "aparelhamento" has to do with the State and public institutions. If I were to "aparelhar", let's say, my whole family against my brother, I'd say "influenciar" or "manipular" (even it involved money) them.
But one can "partidarizar" almost anything, in the sense of making that thing a tool for their political party, as you can see here
https://folha-online.jusbrasil.com.br/noticias/100054815/em-... This person is accusing other person of using their church to their own political/electoral gain. Almost as they were "politically weaponizing" a church (something that, in theory, should not be partidarizada). The State is always "partidarizado" because there's always political parties on command. And I wouldn't say we use the word "partidarizar" that much in PT-BR.