Does severance delay my unemployment claim?, customer-service rep here

I was offered severance of 8 weeks after being let go as a customer-service rep and I am unsure how it affects benefits. There are 8 people counting on me, so I am trying to be careful. I also wonder about the job-search requirement.

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.