Move code to simplify ScreenshotController

Removes unused method from ScreenshotController and moves inner
classes/interfaces that are only required for SaveImageInBackgroundTask
to the latter, to simplify ScreenshotController in preparation for
rolling out the flag that will remove SaveImageInBackgroundTask.

Bug: 328603973
Flag: EXEMPT moving code/removing unused code
Test: manual, atest
Change-Id: Ib89ccebb292dd65a804379d9ec12faa19125c75c