You can delete your account. They do retain PII for legal and tax purposes.
The retention section offers more detail:
"Etsy will retain your information only for as long as is necessary for the purposes set out in this policy, for as long as your account is active (i.e., for the lifetime of your Etsy member account), or as needed to provide the Services to you. If you no longer want Etsy to use your information to provide the Services to you, you may close your account. Etsy will retain and use your information to the extent necessary to comply with our legal obligations (for example, if we are required to retain your information to comply with applicable tax/revenue laws), resolve disputes, enforce our agreements, and as otherwise described in this policy. In addition, Etsy sellers may also be required to retain and use your information in order to comply with their own legal obligations. Please note that closing your account may not free up your email address, username, or shop name (if any) for reuse on a new account. We also retain log files for internal analysis purposes. These log files are generally retained for a brief period of time, except in cases where they are used for site safety and security, to improve site functionality, or we are legally obligated to retain them for longer time periods."