The European Union’s traditional August break was supposed to provide officials with some respite ahead of a potentially bruising autumn when it will try to set its fiery trade relationship with China on a new course. Instead, a border crisis on its southern flank has created turmoil and division among its 27 members, raising questions over how prepared the bloc is for a dust-up with one of the world’s economic superpowers. “We had a real-time test of what happens when one member state was under...