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.
Please forgive me, as a Debian user I’m prone to senior moments and will soon have my driving license legally revoked.