And they have an advantage in that they own the biggest global media production and distribution houses. They can just pay some Hollywood producer a few million to insert some anti-China lines or propaganda in random movies or TV shows and it goes global just like that (though it's usually a bit more complex and would involve wining and dining various people via think-tanks paid to to do this and sharing talking points with them). And China has no real power to push back on that outside its borders and given its foreign policy of non-interference they couldn't if they wanted to without doing a dramatic change there.

Compare to the US reaction if China tried shopping around a TV series or show that had some minor anti-US and pro-China sentiment? US and aligned media across Asia would light up screaming about it being China propaganda, about how it has to be censored, about how weak any given country will be if they allow it to be shown and stirring up a shit-storm over it. So the US is definitely able to actually make use of their dollars here and get good value. China by comparison can spend as much as they want on shoving propaganda into products, the US will handily get a large chunk of it censored or subject to boycott.

People need make no mistake. This will go to think-tanks who will produce slander which is picked up by western and non-western news and ran near verbatim as stories. They will create chains of citations and credibility in academia and in the NGO world about China being up to no good. This will filter into western and non-western media, public consciousness, etc. It will likely end up nearly as complete as the propaganda about the USSR was for Americans and the western world. Just like indoctrinated Americans who can go to the DPRK and see what they want to see instead of the reality, even travel will not dispel this for many and at that point the task is simply to make it impossible to challenge their narrative, for any westerner who speaks truth to be cast as mad, as a bot, as a propagandist, as indoctrinated by China, as fooled by potemkin villages, as gullible, naive fools.

And that's just the west, their real goal is to propagandize to Africans, to people in Asia, to potential partners of China, to undermine the material goods Chinese projects do with suspicion, lies, and fantasy about what it's all /really/ about to create space for the US to drive a wedge and to operate, to create terrorists and coups with some amount of popular support to remove China-friendly governments and replace them with US friendly puppets. Such is the problem of short human lives. Though the older generations may remember and know of what the colonizers did, the young may buy the "that was the old us but we've changed" routine the US has so perfected. And without class consciousness this can work.