Non-compete clause

I was hired as a full-time salaried Behavior Analyst, but the company’s non-compete clause says I can’t work for any competing business (it doesn’t specify whether that’s only during employment or after).

I planned to take a small part-time role on the side. HR told me I wouldn’t be able to hold two jobs since they can’t reliably track whether I’d be working elsewhere during their hours. I have another call scheduled to clarify that it would only be outside my scheduled hours.

Has anyone dealt with something similar? I’m in NY. Any insight would help.