New revelations showing how Gen. Mark A. Milley, the nation’s top military officer, quietly maneuvered to check President Donald Trump reveal the lengths that top officials went to prevent potentially rash action, but the disclosures also threaten to thrust the military deeper into the partisan fray, former officials said. A series of dramatic inside-the-room accounts, including one in which the chairman of the Joint Chiefs promised to alert China’s top officer if Trump was preparing to launch an attack, provides new insight into military leaders’ response to the previous administration’s fraught final period.