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Best FOSS Local Messenger Service?
(beehaw.org)
If it's free and open source and it's also software, it can be discussed here. Subcommunity of Technology.
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Two ideas:
xmpp works, but the domain needs to resolve correctly. I'd just use a free domain that you point at the server LAN ip, plus an acme client that can do a dns challenge. Prosody is pretty bulletproof and very lightweight.
deltachat + email. Set up a little IMAP server for the lan and use Delta chat to create a messaging over it. Or just use an email client.