For example, this channel is federated from Peertube as a Lemmy community. If you look at the community’s sidebar, there appears to be no moderator for the community; is this a federation issue? I would assume that the channel owner is responsible for moderation (of comments, as posts being allowed is technically a bug), but they aren’t listed.
Lemmy to Lemmy moderator actions all federate, however it gets flaky with Lemmy to Kbin/Lemmy to Peertube/Lemmy to Mastodon (and vice versa) where each different activitypub implementation have their own unique moderation commands AFAIK.
Reports on Lemmy were not federated the last time it was brought up in a discussion, no idea if that has changed now
Everything else mentioned is 100% correct though, lemmy instances can also moderate communities that are federated to their instance, albeit only their instance users will see those changes.