Severance and unemployment, do they overlap? after 13 years as a line cook

I was offered severance of 13 weeks after being let go as a line cook 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. Who should I ask before signing?

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