That's why I called them quasi-public squares. That said, they are run and managed as private companies with shareholders and profit motives. They are not government owned nor regulated (phone companies and ISPs often are). If and until the law changes, such platforms are entitled to regulate how they would like, suppress what they want, ignore fact checks, push garbage, etc. Facebook and X in particular have chosen not to regulate content at all any more, which is why they are now pushing the worst of the worst to the forefront. Clicks make the money.
The text of the 1st amendment is very clear though in that regulating speech only applies to the government, specifically Congress. The test SCOTUS therefore has to apply if any such law is enacted is called "Strict Scrutiny" (the government must show that its actions were “narrowly tailored” to further a “compelling government interest,” and that they were the “least restrictive means” to further that interest.). For example, someone can't make a bomb threat in an airport, that is not protected speech.
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."