“The short answer is: it depends. Whether you are driving for a delivery app service or a mom-and-pop pizzeria, it will depend on your insurance provider.
Depending on your insurance company, you may need a commercial policy instead of a personal policy to use your vehicle for business, even infrequently. If you are not covered for deliveries, your insurance company will deny coverage for the claim. They would send you a written denial of coverage when their investigation is complete.
You may be able to file a claim through the other party’s insurance. This would depend on your state’s comparative negligence laws.