Severance and unemployment, do they overlap? - 23 weeks in

I was offered severance of 4 weeks after being let go as a recruiter and I am unsure how it affects benefits. I would rather hear the honest version than the polite one. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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