The government wasn’t found to be suppressing information, it is just an injunction. The government claims to simply be engaging in dialog about areas they find concerning from a variety of angles including salient public health in a declared emergency, what is considered to be dangerous medical advice, participation in conspiracy and sedition, influence of elections, etc. The injunction, as the article describes, doesn’t prevent the agencies from engaging on a lot of these topics and the topic set is somewhat narrow. The government generally has been allowed to constrain speech that’s a clear danger or interferes with either the goals emergency operations or the safe conduct of emergency operations, as well as public health and safety. This has been upheld in case law and by the Supreme Court for over 200 years.

I’d note that a Trump appointed judge in Louisiana giving a preliminary injunction on something uniquely ideologically aligned by those dimensions and is noted in the article as out of step with precedent isn’t the end of the line.