Prepare Private class of TreeView for sharing with TreeWidget

Move most logic from TreeView to methods of the Private class. Only
TreeView::focusInEvent and TreeView::moveCursor are left as-is because
they call protected methods and methods of the super class which cannot
be easily done from the Private class.

(cherry picked from commit 36bf091e09b8bee6efde72e2a2647da9d6146e58)
(cherry picked from commit 495458f05289aff9a76ec40b89a0d55acf13ec80)

• GnuPG-bug-id: T6568