[2/n] Move new picker logic to AOSP am: 5198aca210 am: 4c95288154

Original change: https://googleplex-android-review.googlesource.com/c/platform/packages/apps/WallpaperPicker2/+/14909766

Change-Id: Ica53120d4d2f06dd1233b62b89949164598d9066