Arguably, its more like non-compete agreements but with the added fact that state enforcement of the agreements is in tension with freedom of speech.
But, you know, lots of jurisdictions sharply restrict enforceability of non-competes, too.
Read about record contracts. Prince spoke extensively about his restrictive contracts.
Plenty of contracts benefit both parties but are bad for society as a whole, and if the government pre-signals which sorts of those contracts it will refuse to enforce, this is good for society.
This doesn’t limit the Feds. Also, a state can prohibit non-compete. Etc. Basically, the freedom to enter into a contract is not one of the four corndogs of freedom.
The only sensible way to approach libertarianism is to qualitatively evaluate individual liberty. And being prohibited from speaking 8 years after the fact, especially when there is a compelling public interest, is in no way equitable. If they want her continued silence, they should have to buy that on the order of year to year.
If you're making an argument that the right to contract should be unlimited between individuals (and perhaps unlimited between legal entities), but should be limited when made between individuals and artificial legal entities, that would be an interesting framing to explore. But afaik it's not really a popular one.
(although I don't know that such a framework would actually invalidate what I said, especially for autocratic totalitarian states - each citizen of North Korea could just as easily be said to have a contract with Kim Jong Un himself)