On your iOS device you noticed on your app's Messages feature that you received a push notification for your web app (PWA), but you never got an alert for this notification. This article explains why this occurs.
By design, iOS devices receive the push notifications that are destined for PWAs, but they do not notify the device. This means that the users are not notified with any pop-up message on their screens about incoming push notifications. These notifications just show up in the app's messages feature.
Full support is still in the works with Apple, but Apple hasn't announced yet the support of web push notifications.