This has been a stick in our boot since we added push notifications. They've worked fine on Android from the start mostly, but Apple has pernicious rules that we couldn't find articulated well anywhere. We also found bugs with iOS push notifications that we were the first to report, and Apple has been at times hostile toward PWAs, so we thought many of our push notification issues on iOS were just more of their bugs.
After somehow living with them for a year, finding them both annoying and embarrassing, we raised the bounty on fixing them to 3m sats. @Soxasora found some hints at the bottom of some blog posts and some other cross-incompatible issues with the way we implemented notifications.
That's all to say that iOS push notifications should be less buggy now. If you still experience issues with them, let us know again so we can finally get this settled.