I don’t see anything especially wrong with the first article FAIR cites. The NYT article covers actual, serious concerns with the powers of Brazil’s supreme court – not unlike the ones the US’ far-right have used to seize power. For context, this was written in September 2022 before Brazil’s presidential election and therefore the coup attempt:

In 2019, a few months after Mr. Bolsonaro took office, a one-page document vastly expanded the Supreme Court’s authority. At the time, the court was facing attacks online from some of Mr. Bolsonaro’s supporters.

Typically, law enforcement officers or prosecutors would have to open an investigation into such activity, but they had not.

So Mr. Toffoli, the court’s chief justice, issued an order granting the Supreme Court itself the authority to open an investigation.

The court would investigate “fake news” — Mr. Toffoli used the term in English — that attacked “the honorability” of the court and its justices. […]

To run the investigation, Mr. Toffoli tapped Mr. Moraes, 53, an intense former federal justice minister and constitutional law professor who had joined the court in 2017.

In his first action, Mr. Moraes ordered a Brazilian magazine, Crusoé, to remove an online article that showed links between Mr. Toffoli and a corruption investigation. Mr. Moraes called it “fake news.”

At first blush (reading about five articles), Crusoé seems like a super typical politics magazine. It does seem that even if the supreme court used its authority for good to shut down Bolsonaro’s coup attempt, they wield too much power. I didn’t read the rest of the FAIR article, but if that’s the NYT article they have as Exhibit 1 punctuated with its own image and caption, I’m not inclined to take it very seriously.