Japan’s ruling Liberal Democratic Party (LDP) is grappling with an identity crisis, its decades-long political dominance rattled first by a humiliating electoral defeat and now, the anticipated resignation of Prime Minister Shigeru Ishiba.Ishiba, 68, on Wednesday dismissed as “completely unfounded” media reports that he had already decided to step down. But analysts contend that his departure is all but inevitable after the LDP’s second consecutive loss and the collapse of his minority...