I've set up my own Lemmy instance (using @ubergeek77's Easy Deploy script) on an Oracle Cloud free tier. I can sign in, and have added communities from other instances.
I'm seeing new posts from lemmy.ml, but not from lemmy.world. Does it take days to do an initial sync (my instance was created on Thursday)? Is Lemmy.world just too overloaded?
On my instance, everything from them floods through all at once, filling my first couple of pages with hours or even days worth of stuff, then I'll get nothing from them for a while again.
"Initial sync" isn't a thing. Things only federate from communities after you subscribe to it. Old posts will make their way over if someone interacts with it (comments/votes on it). I think old comments may make their way over under the same conditions. Old votes will not make their way over so your vote count on old posts will never be right.
You can search for a post or comment to force your instance to load it (copy the federation link, the rainbow-web-looking icon) just like you would do for communities. I think there are scripts out there that may automate this process to force your instance to load old content, but you're putting more load on an already strained system.
And yes, lemmy.world is probably overloaded. Usually this just means that federation from it isn't instant and may take a little time.