Fix a couple PIP related issues.

- Only show settings button when in the full PIP menu (71709327)
- Fix issue with PIP not moving with keyboard due to new callback order
  (71584422)
- Make home button consistent with recents button when in an activity
  over the lockscreen (64137485).  When you tap home, it will now prompt
  you to unlock before going home (and auto-entering PIP if the app
  supports it)

Bug: 71709327
Bug: 71584422
Bug: 64137485

Test: Manual, ensure that pip shifts with keyboard and verify that it
      launches into PIP from show-over-lockscreen activity

Change-Id: I9122b7e20a5bfe82b32c8b576bd4fa11b5659c31