Severance and unemployment, do they overlap? - any advice?

My employer is paying severance in instalments and I am not sure whether to file now. This is my first time dealing with any of this. The agreement mentions a release and a payment schedule. How did your state treat it?

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

Some states only count certain kinds of severance. A local workforce centre could tell me which.