16. (12 points) In the Cartesian coordinate system $x O y$, the graph of the linear function $y=k x+b+2(k \neq 0)$ intersects the positive $x$-axis and $y$-axis at points $A$ and $B$, respectively, such that
$$
\mathrm{S}_{\triangle O A B}=|O A|+|O B|+3 \text{. }
$$
(1) Express $k$ in terms of $b$;
(2) Find the minimum value of the area of $\triangle O A B$.