Starting with the release of iOS 16.4, Apple will be revising the interface for participating in iOS/iPadOS betas. This is in part to help reduce the prevalence of non-registered users downloading beta releases (which will help reduce the unwanted spread of iOS 17 later this summer), but also to make participating in the beta easier for everyday users. The days of downloading and activating profiles are gone, and in their place is an online check of your Apple ID
