Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 3 weeks after being let go as an operations analyst and I am unsure how it affects benefits. There are 3 people counting on me, so I am trying to be careful. 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.