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

I signed a severance agreement and I am worried about how to report it. I have read a lot of threads here and could not find my exact situation. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.