>If freedom of speech is absolute, then it means that any contractual clause purporting to restrict it is void.

No it doesn't.

>In the same way that any contractual clause purporting to enslave a natural person, even with their consent, is still void.

Such a contract is banned because of how one-sided it would be. Even a contract for selling property can be overturned if it is too one-sided. The difference being is that there are many fair contracts for exchanging property while there are none for enslavement. Compare this to indenture servitude, where some variants are allowed, though they include some way to break away.

Consider that a person owning their own creations, something largely considered quite absolute, does not preclude them entering in a contract where such creations are owned by the other party.

The core difference here is that the government cannot punish you for information you gave or received. You can have a civil case for breaking a fair contract you consented to (and if court ordered damages are not paid, you can then be guilty of contempt of court).