FHC is socialist, although center-left. Haddad is normal left, fully Marxist but not communist.
Lava Jato corruption... well it is complicated. Lula indeed did deserve to go to jail, but news written by Glenn Greenwald, that is married to a politician with ties to Lula, gave fuel for the Lula appointed supreme court to free Lula (and a ton of other criminals alongside him... they kinda buthered the constitution and also created a serious security issue). That said, the news that Glenn Greenwald reported isn't a lie, Lava Jato did had issues, personally I don't think these issues should have resulted in Lula being freed, but the issues do exist.
And about Lula & Haddad, well... I would say your characterization of them is as biased and wrong as you claim the author to be; it's equally ideologically charged, but in the opposite direction.
So the result is that you didn't really show anything wrong with the author, but simply expressed your ideological distaste with his leftism; while we, the readers of both the article and your comment, are left to choose based on nothing more than purely our own ideological inclinations.
Further, how would you categorize Cardoso in the political spectrum? I mean, that is the one consensus about his administration, which encompassed privatization of state services, privatization of banks, outsourcing of workers and other state services, opening of the national market to foreign companies.
And that is a shame, because a more neutral historian would clearly acknowledge that Lula (and the Worker's Party) were given the chance to lead the country into a cultural shift and finally realize a project for the country, but failed precisely because they saw themselves as the "new elites" and played the exact same kind of power games to keep themselves on top.