China is already at propaganda war with them, so it is not a surprise there. This war is not easy, and the Americans are especially good at this. They also have hold of the world media, though the advancement in technology level the playing ground significantly.
There are three significant weaknesses or maybe obstacles for China to win this propaganda war. First, years of censorship made China obsolete propaganda department not very good at this game. Sometimes I feel like when the Chinese propaganda dept release a rebutal or statement, they are just talking to themselves, ignoring what the audiences really want to know. Avoiding the elephant in the room, doesn't make the elephant disappear. Take the debt trap issue as an example. The Chinese spokespeople keep saying that the debt trap issue is not true, a smear. Yet they didn't give much detail explanation to the public of why it is not true. Like Hambantota port issue. The irony is that it is actually western scholars who published their extensive research that rebut the Chinese debt trap hoaxes. Overall, the Chinese propaganda dept give a feeling like they are self righteous, but from outside perspective, they look like arrogant fool. They are also not very nimble. More importantly, the Chinese propaganda dept made me think that they only care about Chinese domestic opinion, but not global opinion about China. As long as domestic audiences calm, they are okay with it. But what about China interest in foreign countries? Who are going to defend Chinese image there?
Second, now I know the west have accused China of wolf warrior diplomacy, but I have a feeling that the Chinese propaganda strategists still avoiding launching attacks and counterattacks against the US, all those wolf roars and no real bites, probably to prevent the relationship from deteriorating further. For example, we never heard the Chinese officials talk in depth about Snowden, or Assange. There are plenty of times when I feel like there is a good opportunity for China to deal a blow to the US image, yet the Chinese officials didn't take the shot. For example, the current crisis in Gaza that the US turn a blind eye to. China can loudly call out the US for not stopping or punishing Israel. Unlike the Russians who hardly miss a chance. Maybe it was rational policy in the past, to prevent the relationship from deteriorating, but the US today is much different than the one in the past. The US hold no punches when it comes to attacking China image, they also have no qualm to lie to achieve that. Just look at their smear campaign against Chinese covid vaccines. I wonder how long China can receive punches without fighting back.
The third weakness, is the action of some Chinese nationalists. Like I said propaganda war is not easy. The first step you need to know is who your enemy is. Propaganda war is a battle of public perception. You need to win the sympathy from public against your enemy. That means sometimes you also need to restrain yourself. China is already at propaganda war with the US and Japan. There is no need to add enemy to the list. Yet, Some Chinese nationalists keep adding enemy to the list over trivial matters. For example, kimchi origin dispute with Korea. I really don't know how the hell that happened. I even suspected that some American paid buzzers disguised themselves as Chinese commentators provoking the internet conflicts.