Unfortunately the library you're using is old and only uses the CardElement and tokens which is no longer Stripe's recommended integration path, and soon all token-based integrations will be deprecated(today only cards are still supported). As you can see in https://docs.stripe.com/sdks/community, Stripe recommends using vue-stripe.

As for the integration flow that suits best your use-case, I recommend looking at the deferred flow and just replacing the front-end part with the vue-stripe components.