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

I was offered severance of 13 weeks after being let go as an HR coordinator and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. I have a mortgage and need to plan. Did you file straight away?

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