They save the information to your profile, it'll pop up as "payment verified" on your account and without that you typically "not always" will see a lack in proposals if you don't have it verified.
They don't sell or give out your information though, I've never heard of anything like negative like that on this platform.
If Upwork did not save your information somewhere, they would not be able to charge you for the work done by freelancers you hire.
So the answer to your question is: Yes.
Upwork saves your pertinent credit card information, in the same way that Amazon.com, and other retailers save your information if you set up accounts that can be charged without re-entering that information, and in the same way that Netflix and other subscriptions save your information so that they can charge you on a recurring basis.