Should the onion be diced before adding it to the sauce?

No need! This follows the style of Marcella Hazan's Genius tomato sauce (where the onion halves infuse the simmering sauce): https://food52.com/recipes/13722-marcella-hazan-s-tomato-sauce-with-onion-butter. But you could chop up the onion before it goes in or after it cooks if you prefer.