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This is a really big deal, but it's also a little bittersweet, because Push Notifications very heavily motivate developers to introduce serverside components to apps that don't need them. Web Push is a standard where I can really see Google's influence, and I think it influenced the standard for the worse. It's a standard built around the way that Google and large companies build products, it's not built around indie development or hobby projects.
You can send a notification to whatever server is registered and it gets delivered to the phone, great. In contrast, there is no way for a PWA (unless something has changed since I last looked, in which case PLEASE tell me) to schedule a notification for the future without contacting a server. It's a bad direction to go for PWAs, given that the whole point is for them to be able to work offline.
And yes, sometimes you do need a serverside connection for things like message notifications, but there are a lot of uses for notifications where you know upfront what the notification needs to say and when it needs to be shown -- and that's not supported. In my opinion because Google doesn't really think about that kind of architecture and the idea that you wouldn't contact a server alongside every user action is foreign to them.
There was effort for a while to get offline alarms, scheduled notifications, even scheduled actions working through web workers, but as far as I know that stuff has all died off. It stinks, because I regularly run into scenarios where I could probably flat-out replace an app on my phone with a website, and I can't even on Android, because I'm unwilling to set up an account system and start tracking a bunch of data. I'm happy we have something, but I'm still remembering the parallel world we lost, where it would have been possible to have a much broader push towards completely offline PWAs that never transmitted user data anywhere. The idea of being able to replace native apps with a static Netlify page is very appealing to me.
And maybe that'll change? But I'm not holding my breath; it seems like a lot of companies have decided that push notifications are good enough and that they were going to require user accounts anyway.