Got severance, how does it affect benefits? (update)

I was offered severance of 4 weeks after being let go as a forklift operator and I am unsure how it affects benefits. Any experience at all would help. 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.