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Because it is privately owned. That officials choose to use such a channel for official communications is their responsibility.

From my humble understanding of all of this - Trump was acting as POTUS when blocked people, while Twitter acted as a private company.

You just answered that in your own question :)

Trump is an elected official in the executive branch, and therefore not allowed to restrict the speech of citizens.

Twitter is not an elected official in the executive branch, and therefore is allowed to block people when they see fit.