AMC 10 2021a Problem 9

What is the least possible value of $(xy-1)^2+(x+y)^2$ for real numbers $x$ and $y$? $\textbf{(A)} ~0 \textbf{(B)} ~\frac{1}{4} \textbf{(C)} ~\frac{1}{2} \textbf{(D)} ~1 \textbf{(E)} ~2$