Yes, it’s possible. To be honest, I find it very sad that we have grown so dependent on ISP and big telecom companies to have a working network.

In theory, you could have an infrastructure in your neighborhood and be able to play Quake with your neighbors without making use of the phone line at all, completely free of monthly fees and with a very efficient and fast connection too! you’d just need cabling connecting the apartments/houses and some decent routers controlling/restricting access on each subnet. It’s a pity that’s not a standard thing when designing residences.

Though less efficient and more limited in range, you can technically do it with Wifi and mesh networking too… there are projects like B.A.T.M.A.N (https://www.open-mesh.org/), however, it’s not very user-friendly to set up. I believe there have been some projects that attempted to launch embedded devices to act as mini routers for this, but the spread has not been wide enough to make it worth it, sadly.

Briar has a mesh mode. And i think there was a matrix app doing this too?

If you don’t want to use internet the only ways are to use radio or deploy your own network infrastructure (optic fiber or cell tower), so there’s no really any messaging app that can be used without internet. Briar can use Bluetooth but with a limited range, needing an actual dense mesh network.

Meshtastic can be encrypted and is LoRa based. Can easily hit nodes dozens of miles away with a good line of sight. It also relays messages across nodes to reach even further distances.

Check out Reticulum Network Stack using LORA radio. Works really well.

http://reticulum.network/

The first thing that comes to mind is Meshtastic: https://meshtastic.org/

This one works, if you don’t mind a little diy and texting only: https://circuitmess.com/products/chatter-lora-communication-device

I mean this is a terrible answer, but DS pictochat fits that

Besides the already mentioned Briar, there’s Berty, can’t speak to its quality since I never used it, but I always found the project neat in and of itself

Thereis stuff like

https://meshtastic.org/

https://unsigned.io/private-messaging-over-lora/

wouldn’t a cheap walkie-talkie be more practical in that situation?

i remember using this app some time ago ☞ https://f-droid.org/packages/org.jsl.wfwt/

Isn’t this what airdrop was?

There used to be one years ago that used WiFi radios or Bluetooth or whatever so you could chat to people near you… I totally forget what it was called though.