The freedom of speech is not granted by COTUS, it is a natural right granted to you because you are a human. The first amendment only guarantees that the federal government won't abridge that right and the tenth should restrict the states from doing so as well, though some state constitutions have an analogous right to the first enumerated in their constitutions.
A broader question would then become should an entity such as twitter that enjoys federal protections and carve outs also be bound by the same restrictions the federal government is in regards to speech? Twitter has exemptions and protections that this forum, for instance, does not enjoy. This is question that could end up in front of SCOTUS at some point, which would be an interesting case to follow.
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