Got severance, how does it affect benefits?

I was offered severance of 13 weeks after being let go as an HR coordinator and I am unsure how it affects benefits. It has been weighing on me all week. I also wonder about the job-search requirement. Who should I ask before signing?

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 7 months ago, and it settled down once I kept a simple log of every call and form.