Recommended and mentioned products
Quassel IRC is a modern, cross-platform, distributed IRC client based on the Qt4 framework.
A free and open-source chat client for your website
ConverseJS is also a pretty solid web client, and it's easy to host as well.
An advanced purely-functional programming language
I vote for either staying in IRC or moving to Matrix, preferably haskell.org runs its own instance. I don’t see any better option.
Matrix is an open standard for decentralized persistent communication over IP.
I would also consider https://matrix.org/docs/projects/client/matrix-ircd option. I’m not sure how stable it is but in general it’s an IRC interface for Matrix network. matrix.org maybe even runs some, I didn’t try it. But I’ve tried and still use XMPP bridge for instance. You could join Matrix rooms from XMPP. For instance (these are XMPP MUCs):.