Severance and unemployment, do they overlap? (Nashville)

My employer is paying severance in instalments and I am not sure whether to file now. I would rather hear the honest version than the polite one. 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 4 months ago, and it got easier once I kept a simple log of every call and form.