Severance and unemployment, do they overlap? - 6 months and counting

I was offered severance of 16 weeks after being let go as a payroll clerk and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. I also wonder about the job-search requirement. Who should I ask before signing?

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