The story you are referring to involved the New York Post or its affiliates breaking in to Hunter Biden's laptop (a felony) and publishing his personal correspondence, complete with unredacted phone numbers and email addresses. This violated Twitter's policies against doxxing and dissemination of hacked materials. Characterizing this as censorship is misleading; the story contained no newsworthy information and its publication violated longstanding Twitter policy. It's hard to imagine Twitter functioning without such a policy. I don't see any reason the New York Post should get away with violating it just because it claims to be a newspaper.
The Wall Street Journal, a Murdoch rag like the Post and hardly known for its liberal bias, declined to publish this information, which is why it wound up in the disreputable Post instead. Respectable journalists have ethical standards. Act like thugs, get treated like thugs.
There's an argument that when a platform is big enough, it's a common carrier.
Which article, about what subject?