So it's more a free speech law that avoids censorship.
Copy paste from a reddit comment:
Since no one apparently read the article or paid attention to the actually meaningful quote:
The draft "calls for the FCC to develop new regulations clarifying how and when the law protects social media websites when they decide to remove or suppress content on their platforms."
In other words, this isn't about the federal government removing content. It is about the extent to which social media platforms are legally shielded from lawsuits when they choose to remove content.
The "worst case scenario" of this leaked draft isn't the federal government picks and chooses what content is censored—it's that platforms might have to allow almost every kind of content or risk being sued. Which is the opposite of censorship.
(Please note: I am not arguing in favor of this draft. Only pointing out what it is actually saying sans the rampant fear-mongering going on right now.)