23. D.

As shown in Figure 7, establish a Cartesian coordinate system.
Then $A(4,0), B(0,3)$.
Thus, $l_{A B}: \frac{x}{4}+\frac{y}{3}=1$.
Let the distance from point $S^{\prime}(s, s)$ to line $A B$ be $d=\frac{|3 s+4 s-12|}{\sqrt{3^{2}+4^{2}}}=2 \Rightarrow s=\frac{2}{7}$.
Therefore, the required ratio is
$$
1-\frac{\left(\frac{2}{7}\right)^{2}}{\frac{1}{2} \times 3 \times 4}=1-\frac{2}{147}=\frac{145}{147} .
$$
23. A farmer has a farm in the shape of a right-angled triangle, with the two legs of the triangle measuring $3$ and $4$. At the right-angle corner, he leaves a square area $S$ unplanted, and the rest of the area is planted with crops, so that when viewed from an airplane, the farm looks like a right-angle symbol. If the shortest distance from area $S$ to the hypotenuse of the right-angled triangle is 2, then the ratio of the area planted with crops to the total area of the farm is ( ).
(A) $\frac{25}{27}$
(B) $\frac{26}{27}$
(C) $\frac{73}{75}$
(D) $\frac{145}{147}$
(E) $\frac{74}{75}$