Do not clear the application bottom inset when the virtual keyboard uses
OVERLAYS_CONTENT.
The bottom-toolbar workaround is only required for keyboard modes that
resize Chromium content. Overlay mode owns its keyboard geometry and the
protected keyboard implementation needs the original inset to track the
IME transition consistently.
Keep the existing inset suppression for all non-overlay keyboard modes.
Test: Verified on Android with the bottom toolbar enabled across keyboard
open and close transitions.