@erion @jcsteh Actually there has been quite a bit of progress, Goguma (mobile IRC client) is probably the best representation of this.
https://codeberg.org/emersion/goguma/src/branch/master/doc/notifications.md
You'd need a modern IRC server that has direct support for webpush. I believe Ergo is the only option at the moment.
Failing that the IRCv3 chathistory feature is the next best thing but this requires periodic poling.
And for older servers you'd have to use a bouncer. Soju is a good option for that since it supports webpush.