XMPP is a nice, open chat solution. It works similarly to WhatsApp or Signal, but without a provider controlling everything:
There is not just one central server, but many of them, just like with email.
The server provides:
the domains:
aus-mai.nz
in-mai.nz
wallaustrasse.de
wallaustraße.de
jabbermainz.de
jabber.world
Email accounts with the domains listed above; recommended app for encrypted communication: Thunderbird
Calendar and contacts functionality via CalDAV and CardDAV is integrated
PGP encryption of emails on the server (requirement: a PGP key, which can easily be created and published with Thunderbird)
Jabber/(XMPP) accounts as well, for end-to-end encrypted communication with e.g. Conversations (Android, free on f-droid.org) and Monal (iOS)