"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.