2023 AMC 10B Problem 13

What is the area of the region in the coordinate plane defined by the inequality \[\bigl||x| - 1\bigr| + \bigl||y| - 1\bigr| \le 1?\]

\textbf{(A)} 2 \qquad \textbf{(B)} 8 \qquad \textbf{(C)} 4 \qquad \textbf{(D)} 15 \qquad \textbf{(E)} 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.