Severance and unemployment, do they overlap? (update)

I was offered severance of 8 weeks after being let go as a janitorial supervisor and I am unsure how it affects benefits. There are 8 people counting on me, so I am trying to be careful. I have a mortgage and need to plan. Who should I ask before signing?

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

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