Severance and unemployment, do they overlap? (Tulsa)

I was offered severance of 8 weeks after being let go as a machine operator and I am unsure how it affects benefits. There are 8 people counting on me, so I am trying to be careful. The agreement mentions a release and a payment schedule. Did you file straight away?

Keep everything in writing and save the confirmation numbers. It saved me later.

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