Refactor TaskViewTransitions#startAnimation

To separate different steps of the function that were previously
entangled. This sets the ground for adding instrumentation.

Bug: 402454136
Test: TaskViewTransitionsTest
Test: TaskViewTransitionStartAnimationTests
Flag: com.android.wm.shell.task_view_transitions_refactor
Change-Id: Ib30bb384e248c518d3ed1baffea5e6c50613d975