It’s not censorship unless the government itself is doing the censorship and making people face criminal consequences for disobeying.
If a private entity is doing it, even at the request of a government, it’s not censorship or a violation of free speech unless they were going to face legal consequences for ignoring the government’s request.
The discussion here is about censorship. Infringing the first amendment is censorship, but the converse isn't true. Plenty of things are censorship without infringing on the first amendment.
As an example, Bezos hypothetically preventing his newspaper from publishing negative stories about him is censorship. He is censoring his editors in this hypothetical.
As another example, if Bezos says "everyone who calls me a stupid-head will get kicked of AWS", that would be an attack on free-speech.
My point is that unless something violates the first amendment, I’m ok with it. If Bezos kicks people he doesn’t like off of AWS, I’m ok with it. It’s not a public space. The owner of the private space makes the rules. Just like I can kick people out of my house for similar reasons.
Don’t like it? Host it yourself. If the government tries to censor your self hosted content, then I’ll get up in arms.