Severance and unemployment, do they overlap? (Albuquerque)

I was offered severance of 7 weeks after being let go as a pharmacy technician 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?

I filed on day one anyway and reported the severance honestly. The agency decided what to do about the timing.

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