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.