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

I was offered severance of 12 weeks after being let go as a copywriter and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. The agreement mentions a release and a payment schedule. How did your state treat it?

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