Revert "Partial Screen Sharing - Use new app chooser base class"

Revert submission 23792411-pss-new-chooser-qpr

Reason for revert: Additional dependency collided with ongoing
development. Most of the a11y bugs motivating this seem to be specific
to partial screenshare, so this ended up adding cost to Chooser
development without clearly solving the underlying issue.. Need to
regroup on a more sustainable solution to this.

Bug: 294040231
Test: Presubmits

Reverted changes: /q/submissionid:23792411-pss-new-chooser-qpr

Change-Id: I3a8be177fdd93fc7414e610019476ceeb40c9e7d