We all know Signal, Matrix, Telegram, SimpleX, etc… But if you can’t access the internet you can’t communicate. Pretty logic. But would it be possible, at least theoretically, to create an app that permits to message people even if the internet goes down?
It might be a dumb question I really have no idea to be honest.
It’s not p2p but at least many years ago:
SMS.
If the Internet outage is local then the towers would still work and you’d be able to get texts. I went through a few storms where wired home internet was down, the towers weren’t giving me a data connection (no mobile web browsing or anything), but I was able to send and receive texts.
If you really care about what you’re asking after, do what someone else said and get a radio license. It’s 150 year old technology and every time something happens radio operators pop up some kind of emergency communications or bridge to the internet through repeaters or something.