Not much. In theory if a company acts under the direction of a govt official a court could find that it acted as part of the state. But that takes a very high d

Not much. In theory if a company acts under the direction of a govt official a court could find that it acted as part of the state. But that takes a very high degree of entanglement. If the company is simply persuaded the official has a good argument that isn't enough. You can see the miserable track record of Trump supporters sueing over govt programs to report "disinformation" to social media companies for examples of what isn't sufficient.