Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 17 weeks after being let go as a barista and I am unsure how it affects benefits. I am in Boston, in case local advice matters. The agreement mentions a release and a payment schedule. 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.