Twitter IS a private company, as has been pointed out by those who claim Twitter can entirely do as it pleases w/in it’s own realm, so to speak. HOWEVER, Twitter is bound (as an American company) to American law.
The Constitution is America’s law, certain people disliking that fact is irrelevant.
Even though Twitter is a private company, they DO NOT have the right to violate the Constitutional rights of the people who engage on their platform.
This is true regardless how much Twitter’s present admin may have selective tantrums over the free exercise of those Constitutional rights, or how many may claim Twitter somehow ISN’T bound to the Constitution.