Since you don’t own your Etsy domain, rich pins cannot really work the same way as they do when you claim your own site/store. This is because you cannot really add meta tags within Etsy as you dont own the site.
What you can do is claim your Etsy store on your Pinterest business account.
Keep in mind that rich pins are an added benefit for SEO for your domain, but plenty of people have great results on Pinterest even without them.