Yes, you need insurance coverage for your Etsy or Amazon retail business. While you may not have a physical store where a customer could slip and fall or something else could go physically wrong, you are interacting with customers, and you need insurance for the transaction of selling your product. The insurance you need depends on what you are selling and how you are selling it.
You need general liability insurance to cover the sale and delivery of your product. With a physical store, general liability insurance covers you if a customer or vendor is injured in your store. While that cannot happen to an online retailer with no physical location, other things can. For example, your product or the packaging it is in could cause property damage or physical harm to someone. General liability insurance would cover that. General liability insurance would also cover if another company or person sues you for libel or copyright infringement.
You need property insurance if you have business property in storage. If you keep a certain amount of stock in storage or ready for shipment somewhere, you need coverage in case of fire, theft, or other covered causes of loss.
If you rely on the income you make from online sales, you should have business income coverage. If you experience a covered cause of loss and are unable to continue your day-to-day operations, your business income coverage would cover any potential business earnings you may lose and any expenses that could keep your business running. For example, your business location sustains a fire, leaving you unable to operate. Business income would cover your net income loss.
You need cyber coverage. There are many ways threat actors can access your business and steal your personal information and the personal information of your customers, employees, or vendors. For example, they can lock down your computer system and require you to pay ransom to regain access, or they could steal directly out of your account by posing as your bank or a vendor. Cyber coverage covers so much, including cyber extortion, misdirected payment fraud, and network security liability. Cyber coverage can include the cost of a negotiator, IT forensic investigator, or legal counsel to help you determine how pervasive the breach was and what your reporting responsibilities are.