Hi @QHG,
I think you have a wonderful idea and this is definitely on to a service that Etsy should be providing. I went ahead and spoke to Etsy regarding this. Etsy stated: "There's currently no option to use other gift cards for your Etsy shop as Etsy gift card credits just automatically reflect on your account when you claim them." As you likely already know, the Etsy gift cards are sitewide and not for specific stores. Square and Etsy have a partnership, so I had them log this as a feature request. Fingers crossed!
As there seems to be a growing interest in your business, as customers are buying gift cards, you may want to consider setting up a website with a store on it. On that store, you can likely accept the egift cards generated by Square. I would suggest checking out the e-commerce online store page from Square. You should be able to create one for free and you can provide more of a background on your business to your growing customer base.
