Severance and unemployment, do they overlap? - any advice?

I was offered severance of 3 weeks after being let go as a pharmacy technician and I am unsure how it affects benefits. I worked as a pharmacy technician before this. 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.

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.