Does severance delay my unemployment claim? - any advice?

I was offered severance of 3 weeks after being let go as a copywriter and I am unsure how it affects benefits. I would rather hear the honest version than the polite one. I have a mortgage and need to plan. How did your state treat it?

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.