On Reddit, if I write a post in a subreddit and click Post, it is stored on Reddit’s servers, and anyone with a Reddit account can access Reddit’s servers and see it because we’re accessing the same monolithic system. On Lemmy, I’m currently posting to lemmy.world from a sh.itjust.works account in response to an account from programming.dev. On which of those three independent platforms will this message be stored? How could someone from, say, piefed.social see it? I genuinely don’t understand this fully msyself and I’ve been on Lemmy for a couple years now.

It's stored on all of them. Piefed.social can see them because piefed.social is federated with sh.itjust.works, lemmy.world and programming.dev.