Changed picker to stay as long as chooser is shown

Changed behavior of the picker to remain visible behind
the viewer as long as the chooser is active. When the
chooser is dismissed or an option is selected the picker
will finish.

Test: Manual, verified that picker remains visible until
the chooser is acted upon.

Bug: 32413513
Change-Id: I520e25de19d2290b0e52ce2212856afd6e3ee06e