Severance and unemployment, do they overlap? - 3 months and counting

I was offered severance of 15 weeks after being let go as a bank teller and I am unsure how it affects benefits. There are 15 people counting on me, so I am trying to be careful. The agreement mentions a release and a payment schedule.

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