How to add a product variant selector to theme extension settings

Extensions
1

I know that you can add a product selector, e.g.

 {
      "type": "product",
      "id": "gift_wrap_product",
      "label": "Gift Wrap Product",
      "info": "Select a product to use for gift wrapping",
    },

but we need to add a product_variant selector. How can we do this?

2

A product variant selector does not currently exist. The full list of available settings can be see below.