The trick with Renault Twizy is that it is not registered as a proper car, but rather as some kind of motorcycle with a roof, so it does not have really stringent safety requirements.
Because it is not a motor vehicle by insurance and Legal standards in the USA it does not require a license or insurance to operate. If you are hit by one of these, you’ll find there’s no insurance to cover you other than your health insurance. Underinsured coverage on your auto policy will not apply either, as it would if you were hit by a motor vehicle. Source: this just happened to me.
Generally, while your insurer (health, auto, homeowner, or otherwise) would cover your initial costs, you would get reimbursed by suing the driver of the golf cart that hit you and they would either personally be liable or pay through their insurance company.
The difference is that it’s illegal to drive a motor vehicle without liability insurance. With other vehicles, that can be just as lethal to pedestrians or cyclists, there is no such requirement. In my case, the driver who hit me was homeless with no insurance of any kind.
That's awful, I hope you're recovering and can be made whole quickly. Regarding your under/uninsured coverage, were you outside of your vehicle when you were hit?