Severance and unemployment, do they overlap? - 8 weeks in

I was offered severance of 4 weeks after being let go as a welding apprentice and I am unsure how it affects benefits. 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.

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.