Judge Moraes has had his share of run-ins with Lula, and can hardly be described as a stooge for the Left. What he has been doing is go after Brazil's version of the Jan 6th insurrectionists, whom Musk is congenial to along with other far-right causes. As Germany showed, if you don't go after thugs when they are still in their inept beer-hall putsch phase, it is too late afterwards.
No, the judge's very first action after getting censorship super powers was to censor "fake news" about the official that gave him those powers, which later turned to be "true news".