But once you realise they're sending them everywhere, it makes it look more like they've ramped production up to stupifying numbers (which is China's speciality afterall), and have realised their value in goodwill is far beyond their dollar value.
(or, yes, propaganda - there's not a lot of real difference between PR, propaganda and goodwill. Ultimately, doing something good because the optics benefit you, is still doing something good.)
There’s no way the leadership has thought out all the angles.
The translation you are looking for is "dick swinging" :)
I have no doubt his intention really is to save lives, but a secondary motive is surely also PR. Perhaps the Chinese state had some role in this, as well. I'm not much of a conspiracy theorist, but I could see a possible benign conspiracy like them using Jack as a proxy to distribute these.
If they did it officially, it could be trusted less and the motive would seem more blatant. And Jack of course has enough money to do this himself, but such a big international move might require the approval of the government.
Of course it's PR. It's always PR, probably regardless of what superpower's government is involved. The only difference here is that the Chinese government has more control over and knowledge of what private citizens are doing, so it can be difficult to disentangle private and governmental action.