Apply the expand animation on Private Space

- Using the refactoring that took place in ag/25414154

Bug: 299294792
Test: Verified SearchTransitionController didn't regress by turning off BACKGROUND_DRAWABLES flag.
- Verified QL highlight still works
- video: https://drive.google.com/file/d/15yjBWofebn6m7VgEnLK6kEYqhC_adJQ3/view?usp=sharing

Flag: ACONFIG com.android.launcher3.Flags.private_space_animation DEVELOPMENT

Change-Id: Ib6229b404b48616966f3e6ab6884099b6e4b4023