I think in practice it would show up as an enforcement organization of the government labor department that would have a set of prosecutors on staff to enforce

I think in practice it would show up as an enforcement organization of the government labor department that would have a set of prosecutors on staff to enforce wage theft laws, much like how most cities have a DA and other government prosecutors to go through with criminal court cases. The work load of the PD would be minimal other than to maybe enforce jail transport orders after a court case finishes, it would mostly be about funding a lawyer group in the government.