Severance and unemployment, do they overlap? (update)

My employer is paying severance in instalments and I am not sure whether to file now. I have been trying to stay organised about it. The agreement mentions a release and a payment schedule. How did your state treat it?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.

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