Severance and unemployment, do they overlap? after 3 years as a recruiter

I was offered severance of 3 weeks after being let go as a recruiter and I am unsure how it affects benefits. It has been weighing on me all week. I have a mortgage and need to plan. Did you file straight away?

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