Severance and unemployment, do they overlap? - 14 months and counting

I was offered severance of 4 weeks after being let go as a forklift operator and I am unsure how it affects benefits. This is my first time dealing with any of this. 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.