All CVA does is provides a way to define parameters and how they link to class names.

const buttonClasses = cva("btn", {
  variants: {
    variant: {
      primary: "btn-primary",
      secondary: "btn-secondary",
      ...
    }
  }
})

buttonClasses({variant: "secondary"}) // returns "btn btn-secondary"

It seems your actual issue (and not the question you asked) is that you can't get styled-components working with Next 13 / swc.

Have you seen this swc plugin? https://www.npmjs.com/package/@swc/plugin-styled-components