Hans van de Ven's China at War corrects a bit of a trend of looking at the Second Sino-Japanese War in isolation by tying it in with the prewar ambitions of the Nationalists and Communists and the civil war that followed, and would be my personal recommendation as an introduction to WW2 in a Chinese context. Rana Mitter's Forgotten Ally/China's WW2 is a good look at the Second Sino-Japanese War but does indeed only go into the civil war in brief.

China 1945: Mao's Revolution and America's Fateful Choice by Richard Bernstein also addresses this, along with how American and Soviet pressures influenced the CCP and KMT during the Sino-Japanese War and the buildup to the Civil War.