[E2E test] Fix TabTearingTest and FocusAppFromTaskbarTest

The issue was that after showing Chrome popup AppHandler became unresponsive causing the test to failure. We have to launch app first, then close popup and only after that entering DW mode.

Bug: 430191139
Flag: EXEMPT not needed for the funcitonal test
Test: atest TabTearingTest && atest FocusAppFromTaskbarTest

Change-Id: Ic5dcd05c2281bd9f1a9fc69e724123f53c81102f