I get your concerns. I take similar precautions with PayPal and have my personal PP locked down with a 2FA dongle. Like most of the tech heads here, I know what good online transaction hygiene is and how to minimise my exposure to fraud.
The button here says Stripe. The modal used to have a Stripe logo but now it does not. Probably because folk got confused when buying stuff on "MyCornerStore.com" and the payment page had a different logo and not one that said "MyCornerStore" - so they backed out - when dealing with the very large scale, folk are strange (it's why imho FB are absolute masters of both white UX and dark UX - scale reveals every.tiny.little.thing that causes friction in UX and needs to be fine tuned in order to get folk to do what you want them to do). Either way, I'd guarantee the logo on the modal cause more confusion than it created confidence. Which is a brand thing - an area where PayPal has an advantage at least. Way more brand presence with the consumer and association with safety.
Sure. Stripe lacks the consumer profile that is required to act as the "trusted third party" gateway from the consumers pov. I don't know how this problem should be solved tbh.