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.

As of the time I’m writing this comment literally none of the suggestions made actually matter for the ambiguous goal of “general security and privacy” more than building in a neighborhood or community that meets the occupants desires.

Pick a place with people you want to be around who you trust to look out for you.