If I shut you into a box, not tell you why I did that, not even let you know you were shut in a box and tell you to speak as you wish, do you have free speech?

It is not an open forum. It does not treat speech equally. It is a political tool, not much more than that.
The mere fact the platform itself boosts and deboosts posts based on its own bias by default removes any chance of it being a free speech platform.

Twitter is a private entity, and they have the right to establish their own rules and regulations.

That argument is meaningless. It doesnt defend the claim that Twitter offers free speech. If anything it proves it does not.
Free speech has no rules and regulations.