On Mac, where PWAs and Electron apps are also very common, there are still native Mac apps getting made. They're usually expensive, outdated, and left to die on the App Store, but they do exist. Most of them are a testament to how fragile and unsustainable native app development is, given the choice.
Web push notifications are first-class notifications. They support sound and vibration. Standard notification badges appear on their app icon. PWAs that use them appear in Settings > Notifications. Users get exactly the same controls over them that they do native apps. Etc. https://imgur.com/a/Ofg6oxo
Try it yourself: https://progressier.com/pwa-capabilities/push-notifications
There's also concerns about PWAs on iOS in the EU. For a bit of time it was looking like you would no longer be able to add websites to your home screen, so maybe no more PWA push notifications?
Not a stable foundation to build a PWA on. If it ever does get better I would love to get rid of React Native and just have a PWA.