An inquiry into fake news, including online threats to the court, led by Justice Moraes has jailed Bolsonaro allies and taken down social media accounts.
Critics say this stretches the court's remit into policing and politics; supporters call it a model for the digital age.
The court's role in Bolsonaro's trial, in which Moraes is both a rapporteur and the target of the alleged assassination plot which is part of the case, has led both sides to accuse the other of authoritarianism.
Bolsonaro's critics argue he attempted to install a dictatorship.
His supporters, on the other hand, say the sweeping powers the court has used to investigate the alleged coup and the rioting in the capital, Brasília, are an abuse of judicial powers.
Those who believe the judiciary has gone too far in prosecuting people involved in the storming of government buildings on 8 January 2023 often cite the case of Débora Rodrigues dos Santos.
The 39-year-old Bolsonaro supporter received a 14-year sentence after scrawling "You lost, idiot" in lipstick on the statue of Justice outside the Supreme Court.