How far does our natural right to free speech go?

With your natural right and a bus token you can ride to the end of the line.

Does a private company's right to regulate how its publicly-used spaces are used supercede an individual's natural rights?

Of course, you wouldn't expect to go into a brick and mortar business and say whatever you please without the possibility of them asking you to leave.

Are social media sites publishers, platforms, both, or neither?

neither

These bannings and such are great, these companies are getting rid of their content creators, so then those people will go to places where they can speak freely and the places that censor can be the next Myspace, I wouldn't sweat it.