Twitter is now a private company, but that is besides the point, as it would only provide value to whomever owns it people use it, and they only do that if they can get access to what they value.

And no, to be amplification, Twitter would have to boost certain tweets artificially. It is very unartificial when I get results for searching. Otherwise it is also boosting if I use the municipal library to checkout a book, or buy it on Amazon, at which point amplification is meaningless.

You're taking for granted the existence of communication services like Twitter. Twitter is amplification. You can't walk out your front door and give a speech that millions of people instantly have access to. You can only do that because of the existence of private services like Twitter. And the reality is that you have no inherent right to use those services, they can exclude you from them for any reason they like.

Libraries are also amplification, but they are generally public. When a book is banned from a library, it potentially violates the First Amendment. Twitter is not public, so when a user is banned from Twitter, the First Amendment does not apply.

If and when we have a government-operated Twitter, it will have to offer equal access to everyone, and it will have to tolerate any speech that falls under First Amendment protection. But until then, you'll have to live with the possibility that the private services you use will kick you off because they don't like what you say.