If all you want is "send and receive files across a local network" then I can recommend Magic Wormhole and Magic Wormhole William (depending on which app store

If all you want is "send and receive files across a local network" then I can recommend Magic Wormhole and Magic Wormhole William (depending on which app store you use; e.g. Google Play Store, F-Droid, Homebrew, Debian/Ubuntu APT repos, etc). It will attempt to use LAN if it can and uses PAKE for auth.