I wonder whats the difference between permisions do giant apps like whatsapp, instagram have for notification service.

cause they seem like perfectly integrated themselves into this, while ntfy has to pose itself as battery consuming application

I'm planning to using ntfy for notifications like bitwarden vault backups, if apps are updated.

Probably not permissions so much as proper implementation of push messaging for mobile. Apple created a push message infrastructure and Google followed that allows their messaging infrastructure already running on the phone to multiplex messages for multiple apps without needing additional power for listening.

I use Pushover for email push notifications- it doesn’t have a subscription and using the proper APIs.

FCM (Firebase Cloud Messaging), and Apple's own APN (Apple Push Notifications) work as a single OS level service, and they are multiplexed so that many different apps can route through them with a single connection, even waking your phone/watch from sleep. There are open/de-Googled alternatives like UnifiedPush, but they're not integrated at the OS layer (they run as a background worker thread), and can't match the battery efficiency or sleep-wake capabilities of those built into the OS/low-level networking layer.

If you use ntfy.sh and don't use instant delivery, ntfy uses Google's FCM for delivery, which is what everyone else does. It doesn't require a foreground service and has no battery impact.

ntfy offers you additional options with instant delivery or the selfhostable server. That requires a server connection and does impact battery a little. On my phone it doesn't show up in the list it's so low, but others have reported more consumption

What do you mean by "battery consuming application"? At least the PWA of ntfy can use Web Push, which uses your browser's existing push notification service and should not consume any additional battery.

I've been using ntfy for ages. Doesn't chew my battery too much. Chrome, mail and mattermost are my top. Ntfy gets less than 30 notifications per day.