I learned my statistics in university, not Youtube. You are confusing yourself about residuals.

To make my point in the original post, I held the group scores fixed and extrapolated combined scores based on changing population sizes. This is straightforward. Simple even.

\(\widehat S=\sum_g p_gS_g,\)

Why did I call this "linear"? (Not a "linear model", your term, because it is not). The model function actually tracks the population function. Over the 25-year period, however, this trend is in fact linear because the White-to-Hispanic population trend is linear on that timescale. Over a longer timescale it would not be.