Severance and unemployment, do they overlap?

My employer is paying severance in instalments and I am not sure whether to file now. I am in Milwaukee, in case local advice matters. I also wonder about the job-search requirement.

I filed on day one anyway and reported the severance honestly. The agency decided what to do about the timing.

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.