Implement btn nav auto enter pip2 flow 1/3

Implement most changes in Core to support
the btn nav + auto-enter pip flow for pip2 experiment.

Design of this flow is described in more detail here: go/pip2-transitions.

The change should not have any effects when pip2 experiment is off.

Bug: 298263450
Test: mp droid

Change-Id: Iba32999a55238a0e5e00df37ec9a2ba4db8d7996