Mos def not part of your auto insurance. Although often called restaurant insurance or product liability insurance, it is basically insurance for the operations of your business. I’d talk to any local agents that handle commercial lines. Rates vary all over the place by region. The difference in cost between NYC and a suburban county in PA, for instance, is probably significant.

I would talk to whatever ins agent you use for home/auto, if they don’t write the proper type of policy they can direct you to someone who does

You will need some general liablity insurance, for people that jog into your cart and get hurt, extended into a product liability for people that burn themselves or get sick, etc. I’m surprised the City hasn’t required it of you yet, but I’m not sure they will – I am not familiar with NYC.