The payment information form is generated and handled entirely by Stripe.
As for the translations, there's no need to modify code to put translations in templates. Joomla has a built-in Language override component baked in. You can go to your Joomla Admin Control Panel and click Extensions > Languages > Overrides. It allows you to search by both the constant name (which is what is used in the code) or the constant value (which is what is displayed). Pick the one you want to override and then enter the new text.
We use this feature rather than re-invent the wheel because Joomla has a well-documented function which our module can leverage without needing those who have installed EasyPay (or any of our modules) to be familiar with code.
Translation is not as simple as it should be under Joomla: translation strings exist, but you have to find them in the code before adding them to the language substitution tool.
Would it be possible, at least in your media to list available channels so that people less comfortable with the code can use your module?
On the other hand, just by adding data-locale = "auto" in your code, the form data is translated automatically which is significantly more comfortable.