What precisely is it that God wishes to stymie, and how will confusing their language (Gen 11:7) and scattering them (11:8-9) do so?

The Babelites—very possibly, led by Nimrod—aimed to create a unified and ultimately oppressive monocultural empire that would compete with, and even replace, God. Moreover, the scattering would send men on their way so they would indeed be “fruitful, and multiply; bring forth abundantly in the earth, and multiply therein.” (Gen 9:7)