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.
I personally love Riot and Matrix as a "modern IRC".