Severance and unemployment, do they overlap? - 8 months and counting

I was offered severance of 3 weeks after being let go as a bank teller and I am unsure how it affects benefits. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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

Some states only count certain kinds of severance. A local workforce centre could tell me which.