When the U.S. defense secretary, Lloyd J. Austin III, visited Indonesia in November, he pressed his counterpart there about a deal to buy 36 American fighter jets. He left without an agreement. Just days before, the same Indonesian official, Prabowo Subianto, met with China’s defense minister, and the two countries pledged to resume joint military exercises. Located across the southern edge of the South China Sea, Indonesia, the resource-laden nation with a fast-growing trillion-dollar economy and a large population, is a big prize in the geopolitical battle between Washington and…