> In contrast, Stripe collects also data from webpages that are not payment pages.

Like recaptcha, whether the Stripe code is included on a given page is solely up to the author of that page.

While I may tend to agree with OP's requests for increased transparency, that desire does not lend its support to other claims about how Stripe's code works. Putting it on every page is not required. Unless I am mistaken, putting it on every page is not even suggested by Stripe. Why anyone would put Stripe or any other third-party code on every page indiscriminately, without considering whether it was necessary, is beyond me.