I got 'App not installed as package appears to be invalid' message when trying to install my signed release app manually on Android 12. However, it can be installed in my other phones which are Android 9 and Android 6.
I use jarsigner to sign my apk :
$ jarsigner -verbose -sigalg SHA256withRSA -digestalg SHA-256 -keystore my-release-key.keystore <app-release-unsigned.apk's path> alias_name
And use zipalign to optimize :
$ zipalign -v 4 <path-to-same-apk-file> HelloWorld.apk
I've change my phone setting so that able to install unknown apk and tested with app-debug.apk and it works just fine. For more information, my app is written by using quasar framework and built by using cordova.
On Android 12, you have to use V2 signing scheme to sign your APK. Unfortunately, jarsigner is only v1 signing scheme.
In short, use apksigner to sign your APK in place or jarsigner, or if you use Android Studio, don't forget to check the "V2 signing" check box or define the signingConfig enabling v2 signing.