Severance and unemployment, do they overlap? after 13 years as an event coordinator

I was offered severance of 13 weeks after being let go as an event coordinator and I am unsure how it affects benefits. There are 13 people counting on me, so I am trying to be careful. I also wonder about the job-search requirement. Did you file straight away?

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