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.

Hadn't seen this before. Looks nice. I tried the demo, smooth other than the /j is not an alias for /join, which I think is an obvious oversight.

> I would run my own IRC server

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?