evol App Verifier can be used to verify apps' signing certificate hashes are correct. For example, if you download an app from GitHub, you can use App Verifier to verify the app is signed by the correct certificate.
Play Integrity is a completely different thing. Google tries to sell it to app developers as a way to improve security, but really:
The clear real purpose of the Play Integrity API is to degrade Android app compatibility for any device or OS that's not partnered with Google as part of their illegal licensing system for GMS that's used to enforce their monopolies on search, ads, Android app payments, etc.
https://grapheneos.social/@GrapheneOS/113623722061116606