Is there an IOS/Apple app for IRC that acts like an messenger app? (eg persistant connection)?
There is, but it's probably not quite what you were expecting: ZNC
Pair that with a regular IRC client and you're good to go. Suggestion: https://apps.apple.com/us/app/palaver-irc/id538073623
And yes, this is exactly what you'd have been doing when you wanted a persistent IRC connection on *any* system: Use an IRC bouncer. Even if that bouncer is just a screen or a tmux session on a shell server.