You won't see an automatic notification with iOS 14.7 Public Beta to move to iOS 15 Public Beta. So if you want to grab the iOS 15 Public Beta (now available - this is not the dev beta version), then follow the instructions at the link below.
Read them carefully, as you also need to remove the iOS 14 Public Beta profile.
See
How to Install the iOS 15 Public Beta#
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appleAfter promising to release iOS and iPadOS 15 to the public in July, Apple today seeded new iOS and iPadOS 15 beta updates to its public beta testing...