Profiles, yes that’d be nice as that’d bridge the gap with Mastodon and enable users to do standalone posts but see it threaded instead of the horrible microblogging UX for that.
Chat, I don’t think belong to ActivityPub, it works alright for direct messages but that’s it. It wouldn’t scale well for this amount of traffic for a chat. But you can however put your Discord/Matrix/IRC on your profile, and communities can put their own Discord/Matrix/IRC rooms link in the description to form a chat community around the Lemmy community. Maybe an option would be adding dedicated fields for those so that it can be added to the UI to direct you to those transparently. UIs could implement some support for those and embed the chat rooms in the page.