Does severance delay my unemployment claim?, hotel front-desk agent here

I was offered severance of 3 weeks after being let go as a hotel front-desk agent and I am unsure how it affects benefits. I am in Chicago, in case local advice matters. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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.