Pay button + checkout: open specific page after payment was successful

Did you read the Wix Pay API and Wix Pay Backend API sections as there are code examples there that can help you.
https://www.wix.com/corvid/reference/wix-pay.html
https://www.wix.com/corvid/reference/wix-site-backend.html

Along with the Thank You Page API itself.
https://www.wix.com/corvid/reference/$w.ThankYouPage.html

https://www.wix.com/corvid/reference/wix-pay.html#startPayment

Start a payment on button click with a custom thank you page

/**************************
 * backend code - pay.jsw *
 **************************/

import wixPay from 'wix-pay-backend';

export function createMyPayment() {
  return wixPay.createPayment({
    items: [ {
      name: "Product Name",
      price: 9.99
    } ],
    amount: 9.99
  } );
}

/********************
 * client-side code *
 ********************/

import {createMyPayment} from 'backend/pay';
import wixPay from 'wix-pay';
import wixWindow from 'wix-window';

export function myButton_click(event, $w) {
  createMyPayment()
    .then( (payment) => {
      wixPay.startPayment(payment.id, {"showThankYouPage": false})
        .then( (result) => {
          if (result.status === "Successful") {
            wixWindow.openLightbox("Success Box");
          } else if (result.status === "Pending") {
            wixWindow.openLightbox("Pending Box");
          }
      } );
    } );
}