Severance and unemployment, do they overlap? (update)

I signed a severance agreement and I am worried about how to report it. I worked as a security officer before this. The agreement mentions a release and a payment schedule. Did you file straight away?

Some states only count certain kinds of severance. A local workforce centre could tell me which.

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.