Please point out some American media claiming we should go to war with China. That's just a ridiculous statement. There is no amping up for offensive war with China. There is plenty of amping up of concern that China will invade Taiwan and that we'll likely need to defend them. However the US is actively trying to prevent that from happening by being loud on the global stage and actively trying to show that the US doesn't respect China's territorial claims to prevent that type of thinking from rooting in China's psyche.
Ironically I think the Ukraine war has shown the best demonstration for China on why they shouldn't attempt a Taiwan invasion. Their rhetoric about Taiwan I feel has gone down since that war started.
That's why I said "subtly" and "written between the lines". War propaganda doesn't work by overtly saying "Hey, guess what, we should go to war". It builds up little by little, starting with plausibly innocent imagery (for example, picture of Country X's leader, then picture of Country X's military, then picture of Our Country's military--just that silent video montage gets into people's subconscious and starts doing its nasty work). Then it works its way up to insinuation and innuendo, then little "facts" come out here and there, then the hypotheticals. This is exactly how the US public was slowly marinated in preparation for the Iraq war.
No, it really isn't overt usually. Not at first at least. You don't start by beating the war drums openly, it just doesn't work. It's a more subtle, gradual work of normalization before the more overt stuff.
Ironically I think the Ukraine war has shown the best demonstration for China on why they shouldn't attempt a Taiwan invasion. Their rhetoric about Taiwan I feel has gone down since that war started.
The US is trying to avoid war, not start one.