They’re “notifications” in common speech but there’s also stuff like “now playing” and live activities and rich content that are also “notifications” but do require the app to run.
From what you're saying, it doesn't sound like the OS-based polling would be more power efficient, as someone in this chain suggested, just more reliable. Though, I think you can just turn off battery optimization for the ntfy app, in which case I'd expect them to be on par.
If that's right, it seems like ntfy with battery optimization turned off is effectively a "real" push notification system.