This is true for what the government can do legally that infringes on your right to free speech. Yes they can violate your first amendment rights in that case.

However, this does not apply at all to private companies. They could, theoretically, have ridiculous rules “Everyone must refer to themselves in the 3rd person or we ban you” and it is totally legal because it is their platform. 1st amendment applies to private companies only to guarantee their OWN right to free speech.

Correct. You can't falsely shout "fire" in a crowded theater, you can't obstruct an existential war, you can't spread anti-vaccine propaganda during a pandemic.

These are all legal arguments with a well-established history.