“Bureaucrats” and “coordinating” are nice wiggle words because they make your description 100% uninterpretable. It’s convenient because if you put meaningful words there instead, it’d be obvious how weak the complaint is.
The case is about government officials requesting content moderation and about private companies utilizing their First Amendment rights, at times to deny with government requests and at times to comply with government requests.
The government’s right to request content moderation is extremely, extremely well-established in the US. Private companies’ right — in almost all cases — to decline those requests is well established. Companies’ right not to be harassed by excessive requests or coerced by threat (implicit or explicit) is also well established.
This case is just making the argument that if a government requests action or brings a platform’s attention to some content, if the platform agrees with their request, acting on that request or notice would violate First Amendment rights of the people who posted the content.