All the things you describe are achieved via 'bouncers' or dedicated clients living in a server that an impermanent consumption device like a mobile phone might be able to connect to.
No, they're not native to the protocol, nor are they required. However it's an open protocol. You are free to pick from a number of solutions that compose that goal.
I don't want to compose anything and neither does 99% of the world. It's a non solution and we're having the Dropbox announcement discussion 15 years later.
Then buy from a commercial service, just like many do for email. (Many more just use gmail in that context.)
Commercial IRC services? IRC Cloud comes to mind as one I've seen others use. Couldn't tell you how much it costs, how good it is, or if it leaks data.