So, what is a "Visual Approach"?
This from the UK Manual of Air Traffic Services Glossary:
Visual Approach An approach by an IFR flight when part or all of an instrument approach procedure is not completed and the approach is executed with visual reference to terrain.
In your case, NJ, (although not in UK, I know) you were IFR and part of the instrument approach was not completed (due to the Approach Ban plus being visual). You executed the approach with visual reference to terrain.
If ATC were happy with that, and it seems they were, then only some more limiting company rules could put you in the wrong, it seems to me. As to a specific "cleared visual approach" statement from ATC, I'd say that was implied from what you have told us.
An Approach Ban, of course, can only prevent an Instrument Approach.