2.2 Use startTransaction for reparenting when available.

Trying to make each of the CLs as small as possible to keep them
digestible and low risk. For the refactor plan see
go/animlib-shell-refactor-plan.

Bug: 397180418
Flag: EXEMPT simple refactor
Test: atest ActivityTransitionAnimatorTest + manual
Change-Id: I5e6168bda601539f43ce93bdd56fa5351a8a0b6c