(Worked Solution)  I am using iPhone X and I am on iOS 15.1. I tried many options but the one worked for me is to reset Location and Privacy. (Settings -> General -> Transfer or Reset iPhone -> Reset -> Reset Location and Privacy).Once the reset is done, I restarted the phone. Now when I open any app it will ask for all permissions including notifications.

Hello!! I had the similar problem with Notifications in my iPhone and when I reset my location and privacy settings all apps started to request for permissions. Once I accept the permissions, I started to see apps in Settings-> Notifications. Hope this helps.