Record initial app given importance

To allow users an easy way to 'go back to how it was'

(also migrate some tests to other files)

Test: atest, cts
Bug: 135751328

(cherry picked from commit 03de363ce278b6d708a6d30f83468584a14a65d5)

Change-Id: I949f366410d2cb2ab424b1b03222743e6e60d867