I guess the easiest way to add some kind of information into the payment methods selection list will be to overwrite the
templates of each of the payment methods which are rendered in that list.
Magento_Checkout/view/frontend/web/js/view/payment/default.js - there you find the methods like
getTitle() used in the templates) and a html template which is rendered by this renderer.
For example the payment method 'Check/Money order' (checkmo) has the method renderer
Magento_OfflinePayments/js/view/payment/method-renderer/checkmo-method.js and the template file
You can overwrite those templates by copying them into your theme folder and make your changes.
For a better understanding of the payment method concepts you may read the documentation of how to create a cutsom payment method https://devdocs.magento.com/guides/v2.3/howdoi/checkout/checkout_payment.html