What does Bureaucratic Arts II do?
Bureaucratic Arts II allows the player to obtain more types of permits from the Bureaucrats in Bureaucratic Halls. As of now, the only item this enables you to obtain is the General Building Permit, which is consumed in certain phases of Street Projects. BA II is also required in the work stages of certain projects. tl;dr: BA II is only useful for Street Projects, and it is only rarely useful.
It is hinted that in the future more types permits will be added. For example, in the forum post introducing Party Packs, the developers hinted that Parties will in the future require Party Permits which presumably will require BA II to obtain. There also exists the unimplemented skill Bureaucratic Arts III, which hints that the developers may expand the skill tree in this direction in the future.