Severance and unemployment, do they overlap? after 17 years as a sales associate

My employer is paying severance in instalments and I am not sure whether to file now. I worked as a sales associate before this. The agreement mentions a release and a payment schedule. Did you file straight away?

Thanks for writing this out. I went through something close to it 11 months ago, and it settled down once I kept a simple log of every call and form.