Basically not by that example, unless SCOTUS somehow decides to go against their previous rulings on how far one can extend the notion of "government". The most recent relevant case is MNN.
Manhattan Community Access Corp. v. Halleck, No. 17-1702, 587 U.S. ___ (2019), was a United States Supreme Court case related to limitations on First Amendment-based free speech placed by private operators. The Court held that a public access station was not considered a state actor for purposes of evaluating free speech issues in a 5-4 ruling split along ideological lines. Prior to the Court's decision, analysts believed that the case had the potential to determine whether limitations on free speech on social media violate First Amendment rights. However, the Court's narrow holding avoided that issue.
It's also worth noting the grounds for the dissenting (minority) opinion in that case:
The dissenting opinion, written by Justice Sonia Sotomayor believed that MNN “stepped into the City's shoes and thus qualifies as a state actor, subject to the First Amendment like any other." Justice Sotomayor also argues that since New York City laws require that public-access channels be open to all, MNN also took responsibility for this law with the public-access channels. It did not matter whether the City or a private company runs this public forum since the City mandated that the channels be open to all.
But it's harder to see how even that reasoning (which did not prevail for a public access [cable] TV station) could apply to Twitter, Amazon etc. E.g. there's no law or regulation that "Twitter be open to all" in return for some government benefits to Twitter (like accessing some cable monopoly/infrastructure). The nature of the web/internet makes it harder for the government to use something as "legal leverage" for (say) demanding broad access for every would-be user in exchange.
In cases involving free speech claims vs private property rights, SCOTUS has almost always sided with the latter. A prior case (1972) involved leaflets distributed on a shopping mall. Only back in the 1940s there was a case in which a company-town street was judged as a place where government-like free speech rules should apply (and even that was a 5-3 split decision).