I've been using https://www.irccloud.com for years, it takes care of all these things and also has an app / push notifications. It's still IRC, but it takes care of a lot of the annoying parts of it that made it feel dated.

I never worry about presence in any form of chat. I don't care if people are there when I message them; it's up to them to pick up my messages at their convenience.

The Lounge https://thelounge.chat/