Ive never received any QF check-in notifications from the app for cancelled flights (and there have been many) maybe that is an iPhone issue, I'm on Android.
I've also only ever received QF app notifications when online, if roaming with data turned off I don't get check-in notifications from the app unless on wifi.
On Android in order to receive push notifications you need to have a data connection, they are not pre-stored in the Android OS.
Some people may give permission for app to update their calendars which might send an off-line notification but I don't allow notifications from calendar.
As far as the other point about the app not working when the Internet connection was fine, try force-closing it and restarting it, that will usually fix that. If not, it probably means the Qantas servers were down.
I did force close it, made absolutely no difference. Also cleared app data and connected to nearby wifi. Something weird was going on with only that QF app only on my phone as I was able to use email, google and other apps at the time without issue.
I know the QF servers were not down,
as I stated upthread the same QF app on my tablet (also 5G) allowed me to check in when phone wouldn't (both on same mobile provider). This is why I always travel with more than one mobile data capable device.
There must be some random backend setting embedded in QF app that logs you out after a specified period of time and something went screwy on local install to fail to recognise network to get back in. Uninstall/Reinstall (same app version) was only thing that resolved it.
If force quitting and clearing app data cache doesn't work, uninstall/reinstall as I did is next obvious solution.