SAI is an advanced APK installer with split APK support. It also has simple app backup/export functionality.

SAI can install apps using standard Android API using root access or using Shizuku.

SAI is an open-source app you can get the source code on its GitHub repo - github.com/Aefyr/SAI

Please note that SAI only installs user-provided files and is not responsible for those apps behavior.
Please also note that some devices/ROMs aren't supported by SAI that has to do with bad Android API implementation in said ROMs and can't be fixed on app side.