Stratified bundles on the Hilbert Scheme of $n$ points

Let $k$ be an algebraically closed field of characteristic $p>3$ and $S$ be a smooth projective surface over $k$ with $k$-rational point $x$. For $n\ge 2$, let $S^{[n]}$ denote the Hilbert scheme of $n$ points on $S$. In this note, we compute the fundamental group scheme ${\pi }^{\text{alg}}(S^{[n]},\widetilde{nx})$ defined by the Tannakian category of stratified bundles on $S^{[n]}$.