Test flaky test: Always wait for handle task to complete

- Previous logic of checking queue to wait or not has race as queue can be
  emptied while posted task is not complete.
- Do not check queue and always wait for new post to complete.

Bug: 129896850
Test: Run the test many times
Change-Id: Ie0e4447cf997cbe343c7e00a8dfd0757b061b547
(cherry picked from commit 819d7406)