Not sure what you are looking for, but two things come to mind firstly Meshtastic as a system that doesnt use the already existing Internet infrastructure and secondly i2p as a system that uses the existing Internet infrastructure.

I think you’re looking for meshtastic though

How about Mailcow? I mean you don’t need to actually create the Mail Server in order to use Calendar. The setup is pretty straight forward

https://docs.mailcow.email/