I am confident, on the basis of private information I can't share, that Anthropic has asked at least some employees to sign similar non-disparagement agreements that are covered by non-disclosure agreements as OpenAI did. 

Or to put things into more plain terms: 

I am confident that Anthropic has offered at least one employee significant financial incentive to promise to never say anything bad about Anthropic, or anything that might negatively affect its business, and to never tell anyone about their commitment to do so.

I am not aware of Anthropic doing anything like withholding vested equity the way OpenAI did, though I think the effect on discourse is similarly bad.

I of course think this is quite sad and a bad thing for a leading AI capability company to do, especially one that bills itself on being held accountable by its employees and that claims to prioritize safety in its plans.