I don't see any compelling reason to adopt Slack. It does nothing that I care about that IRC doesn't do. If IRC completely implodes, I would run my own IRC server.
IRC is horrible on phones (shitty history when you drop out of an internet connection, no cross-device unread-count synchronization, no encryption or login, etc). There are add-ons that try to fix that, but it's still a giant pain.
I personally love Riot and Matrix as a "modern IRC".
The Lounge is an IRC client that solves the problems you describe (persistence on any device, synchronised unread counters, push notifications) - https://github.com/thelounge/thelounge
It does require having your own server to host it on though.
That's nice for you personally, but how does running an inhouse bespoke IRC server have anything to do with whatever line of business your company is in?
I personally love Riot and Matrix as a "modern IRC".