Severance and unemployment, do they overlap? (update)

I was offered severance of 8 weeks after being let go as a social media manager and I am unsure how it affects benefits. I also wonder about the job-search requirement. Did you file straight away?

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

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