Getting messages should not/does not have anything to do with running in the background.
If you're trying to run standard irc and appear online as much as possible, that's not going to work in iOS without a bouncer to stay online for you and send push messages to send notifications and allow the app to run for a bit to download the messages.
It's probably not a bad idea on Android too, it's technically possible to run as a background service and stay connected, but there's a lot of uncertainty, because other services can crowd you out, and you're at the whim of Google and oems with power management these days.
IRC isn't a well-designed protocol for this use case, and a "land-side" bouncer that bridges the chatty protocol to a lazier protocol ought to be more energy-efficient overall.
... and maybe your own hardware to run them on. But I wouldn't expect any major player competing against other companies to do the work for you when the outcome is supporting some chat protocols that most people don't use.
(Otherwise, if you're expecting vendors to do it for you, you get to expect the lecture that comes with that expectation, in the form of APIs designed to minimize the ease of doing the wrong-for-the-average-utility-of-the-platform thing. Your cell radio could probably be adjusted to operate as a spark-gap transmitter also, but I don't expect them to provide an easy API for that either ;) ).
IRC isn't reliant on a proprietary push message API, though (be that provided by Apple or Google).
I'm sure there are long-lived bouncer plugins that will integrate with said APIs, but the core IRC protocol is not suited to or designed for devices that aren't capable of a long-lived connection.
This idea that the end device should do all the work is not a sustainable approach. There should be a server side component that is handling this for you and sending push notifications when your app needs to wake up for new data.
How do you think push notifications work? There isn't some magic in LTE to wake up your phone. Your phone needs to keep a connection open in the background and periodically wake up the modem to check for new information.
I use Conversations (XMPP client) on Android, it keeps a plain old TCP connection open in the background and honestly it does not much battery at all. It's consistently at the bottom of battery usage according to my phone.
It's a lot cheaper to keep an LTE radio on in a low-wattage "ping me if you need me" mode and trust the 'infinite-power' landside terminal to notify you of messages than to wake it up once every N seconds to loudly ping a cell tower "HEY LET ME KNOW IF I HAVE ANY MESSAGES KTHX."
There’s a very distinct difference between having a persistent connection that only transmits data when there’s something notable vs having a connection that constants pushes a kitchen sink of data that may or may not be needed. Sure, if you sent a push notification on every single message and status change on the IRC server, it’d likely use the same amount of (or maybe more) battery, but who does that?
In that case, having the app run the background really does seem like a waste when compared to leaving the OS to do this task.