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

I was offered severance of 6 weeks after being let go as a bank teller 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. Did you file straight away?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.