Fox "News" is not a news channel. They actually define themselves as "entertainment" so you can't call them out for their lies in court.
This is the weirdest thing liberals believe. There is no such thing as "defining yourself as news or entertainment." There is no legal definition of "news organization".
The lawsuit you're going to reference said that Carlson was "opining" rather than stating "facts" which has a legal definition. Legal definitions don't often match with common usage.
And you can "call anyone out" for lying whether they're a news organization or not.
There was another lawsuit wherein Fox stated that they only showed news for a total of something like 4 hours per day. Some time in the morning and afternoon. Everything else was considered entertainment (despite being displayed as “news”) and therefore had no journalistic obligations (I.e. they could say whatever they wanted). While there may be no clear definition, like you say, journalism has legal protections and responsibilities that are upheld/enforced in courts.
Hannity holds up the start of the forever deficit as an example of how this will cut the deficit. Our brains have tricked down through our heads and out our asses.