dtlib: clean up DT initialization

Initialize all the public API interface related attributes within the
constructor instead of scattering them throughout the implementation
of the class, and make sure they all have type annotations.

Move all the parsing code away from the init routines and public API
down to the main parsing block.

This is for readability and paves the way for later changes that
affect the way initialization happens.

Signed-off-by: Martí Bolívar <marti.bolivar@nordicsemi.no>