I also mostly use Facebook Messenger. In theory at least Messenger should be unaffected by this, since it's a chat app, not "social media". How that will play out in practice, with most Messenger accounts being tied to a Facebook account, is...unclear.
My other big chat app currently is Discord. I've recently started trying to convert one of my Discord groups onto Matrix. Matrix seems pretty good for this kind of thing. It can do one-on-one chats, group chats, and Discord-like "Spaces" with multiple different Rooms. For those less tech-inclined, just don't explain any of the federation details, just go to matrix.org.