But first amendment basically only restricts the government's ability to suppress speech, not the ability of other parties (like OpenAI).
This restriction may be illegal, but not on first amendment ("free speech") grounds.
It does not prevent you from entering into contracts with other private entities, like your company, about what THEY allow you to say or not. In this case there might be other laws about whether a company can unilaterally force that on you after the fact, but that's not a free speech consideration, just a contract dispute.
See https://www.themuse.com/advice/non-disparagement-clause-agre...
Consider for example that when Amazon bought the Ring security camera system, it had a “god mode” that allowed executives and a team in Ukraine unlimited access to all camera data. It wasn’t just a consumer product for home users, it was a mass surveillance product for the business owners:
https://theintercept.com/2019/01/10/amazon-ring-security-cam...
The EFF has more information on other privacy issues with that system:
https://www.eff.org/deeplinks/2019/08/amazons-ring-perfect-s...
These big companies and their executives want power. Withholding huge financial gain from ex employees to maintain their silence is one way of retaining that power.