How does 4chan’s design differ from traditional forums, really? There’s less moderation and more anonymity than you might usually expect, but the very nature of ActivityPub means that aspect doesn’t really make as much sense in a federated forum.
So do you just want something like Lemmy but without nested comments or upvoting, and only sorting posts by new and comments by old, the way a traditional forum does? For that you might be able to try LemmyBB which is a front-end to Lemmy that says it’s supposed to look like phpBB forums. (Unfortunately I can’t verify because the two domains its Readme claims run that software are both no longer active.) Or you could try Morum, forum software based not in ActivityPub but Matrix. There are also plugins for non-federated forum software, like Discourse which aim to enable ActivityPub integration with their forums.
Is there some other feature of 4chan that you want to see?