> Twitter is a private company.

Twitter is a publicly traded company, they agreed to abide by some restrictions by the government in order to get that status.

Do believe publicly traded companies are the same as state or federal public entities that serve the public via taxes? I recommend you look up the difference.

I'm aware of the difference, how does that impact the understanding that publicly traded companies have waived certain rights in exchange for certain legal privileges?

None of those restrictions are relevant to the question of who may and may not use their service.

They are relevant to the concept that they give up certain private property rights in order to gain other legal privileges, which is a precedent for requiring that they give up other property rights (such as the right to censor on the basis of politics, etc.).

Property rights are completely irrelevant to the discussion on hand. 'Right to censor' is a made up concept. Companies and individuals have no obligation to publish something they do not agree with. Anti-discrimination laws also do not protect Trump here. He isn't singled out for his race, sex or religion. He's singled out because he incited a seditious mob that overran Congress.