Severance and unemployment, do they overlap? - 18 weeks in

I was offered severance of 4 weeks after being let go as a delivery driver 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. How did your state treat it?

Thanks for writing this out. I went through something close to it 2 months ago, and it settled down once I kept a simple log of every call and form.