Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 7 weeks after being let go as a project coordinator and I am unsure how it affects benefits. Thank you in advance. I also wonder about the job-search requirement. How did your state treat it?

Thanks for writing this out. I went through something close to it 14 months ago, and it got easier once I kept a simple log of every call and form.