AMC 12 2022b Problem 24

The figure below depicts a regular $7$-gon inscribed in a unit circle.

import geometry;
unitsize(3cm);
draw(circle((0,0),1),linewidth(1.5));
for (int i = 0; i < 7; ++i) {
for (int j = 0; j < i; ++j) {
draw(dir(i * 360/7) -- dir(j * 360/7),linewidth(1.5));
}
}
for(int i = 0; i < 7; ++i) {
dot(dir(i * 360/7),5+black);
}

What is the sum of the $4$th powers of the lengths of all $21$ of its edges and diagonals?

$\textbf{(A) }49 \textbf{(B) }98 \textbf{(C) }147 \textbf{(D) }168 \textbf{(E) }196$