They are actively working on improving the performance. Large distributed systems aren't the easiest thing to build and scale. E.g. here is where they are working on improving the compute time required to handle upvoting:
Its somewhat related, yes. Each time you do something in the web browser like upvote, that gets sent to your instance (e.g. lemmy.world). Then, the instance needs to update the other instances with that action (this is called publishing the action). Meanwhile, it needs to accept actions from other instances (these are actions that the server is subscribed to). All of these actions take server time and network so there is a queue of actions (think of this as each action standing in line waiting for its turn with the network/cpu).
You can optimize this a lot because each time you open a network connection and send something, there is some cpu and network cost above and beyond the action itself. So there are smart ways to group things together. But, the challenge is that such grouping adds delays (e.g. it may take longer for a moderator's removal of an offending comment to propagate to your server).
Yes, sluggishness and timeouts. As others suggest, there are growing pains. I have faith that as the new number of users starts to stabilize, these problems will settle down.