Function $W \mapsto f(W)$ is not convex when $n \ge 2$.
Take for example when $n=2$ and fix $x=1$.
If function $f(W_1,W_2)$ is convex then it must also be convex when restricted to a linear subspace.
Restricting to $W_1 = \begin{pmatrix} x & 0 \\ 0 & 0 \end{pmatrix}$ and $W_2 = \begin{pmatrix} y & 0 \\ 0 & 0 \end{pmatrix}$ then gives $f(W_1,W_2) = x^2 y^2$, which is not convex in (x,y) (this can be checked by computing its Hessian matrix).