Support for Magento 2’s REST API has been added in version 1.4.0 of the official Stripe module. Examples on how to use the REST API with the module can be found at:
Notice how a payment method token is passed to the API at https://gist.github.com/snez/fe4d44ec4729b9f7d6870e50fd8e52b2#file-rest-example-php-L234. If you would like to only test the API calls, you can instead use some of the test tokens available at https://stripe.com/docs/testing#cards
However on a live website, this token should be created at the client-side before the API call is made, using Stripe.js as explained at https://stripe.com/docs/js/payment_methods/create_payment_method. For an example of how the Stripe module for Magento does this, you can review the code in app/code/StripeIntegration/Payments/view/frontend/web/js/view/payment/method-renderer/stripe_payments.js
Also note that your app should handle scenarios where 3D Secure authentication is required by the customer before the order is placed. To test an SCA order, you can use card number 4000000000003063.
With an SCA payment, the module will throw an Authentication Required error. When your app receives this error, you will need to trigger a 3DS modal from your app and then resubmit the order using the same payment method ID. On the second submission, the payment will succeed.