Agreed. As I recall the way notifications work on Signal/WhatsApp is the app receives some silent notification that wakes it up, then the app does its crypto thing, and then it locally triggers the notification with the decrypted content you see. In iOS land your app needs a special entitlement to work this way. It also means if you're on very heavy group chats your battery will drain faster.

If WhatsApp central servers could push a notification to your phone that contained your actual message content, it couldn't be E2EE.

Fair point. For E2EE messaging apps, metadata often includes encrypted message content. As others have stated, the unencrypted metadata (eg. message recipient) can be potentially be damning enough on its own.