In the "food" and "drug" cases, the state does this because large corporations have far more resources available to be applied to the goal of fooling people into consuming something that might be harmful to them, than people have available to figure out they were fooled.
The "news" case, though sometimes being similar to that, is also often very different: private individuals can be sources of news, news is often delivered without cost to the reader, and even news that is sourced from commercial institutions often reaches the majority of its readers through redistribution, without attribution, by private individuals (e.g. word of mouth; posting paraphrases on Facebook; etc.)
So, leaving alone whether the same principle could apply to "news" (or whether it's consistently trumped by free speech concerns, etc.), the implementation of such a policy would be quite different, perhaps different enough as to make it unfeasible. That is a complex question.
Also the USA would not exist if it were not for fake news. It was the arrival of printing presses in Boston which allowed political groups to create fake news to inflame the revolution[1], so it's not always clear fake news is a bad thing (I'm English but I think the creation of democratic America is one of the greatest common goods the world has seen, though i'm sure we can debate that).
[1] Source: https://en.wikipedia.org/wiki/The_Penguin_History_of_the_Uni...
Yes! We could call it the Department of Truth, seeing as we don't have government ministries in the US.
The treatment for misinformation and disinformation is genuine, accurate information.
Censorship and regulation of information is absolutely the wrong way to handle it. If you ever grant any government the power to be final arbiter over what truth is, you deserve what will surely happen to you next.
What precisely is the question?