How do I update my payment method linked to Apple Account?

This is the first thing I tried, and it’s a dead end. I select an issue, and it redirects me back to filling out a payment form. There’s also a button to call, but it says, "We can’t complete your request." There’s no email or form to fill out to contact support. It’s as if there’s no support at all, like the user is completely isolated. Has anyone else had similar problems, and how did you resolve them?

Could this be related to the fact that I haven’t used the account for a long time? More than 5 years, and I’ve reactivated it. Perhaps it takes some time—days or weeks—before I’m allowed to add a payment card?

I am from Ukraine.

Something strange: a card from one bank (Mastercard) adds without issues, but the one from another bank that I need to add (Visa) won’t work. Meanwhile, my friends have the same cards from the same bank added to Apple Pay without any problems. I’ve already contacted the bank; they don’t know how to fix it yet, they’re looking into it, and they say they haven’t encountered this before.

Thank you for the detailed response, Jeff. I’m currently in touch with the bank, trying to figure out what exactly the problem might be. I’m attempting to add a card to my Apple account through a browser since I don’t have my phone with me right now and needed to set it up in advance. The bank says there shouldn’t be any issues at all when adding it from a phone via Apple Pay, but it should also work through the website. Perhaps Visa can only be added via Apple Pay. I don’t see any other reasons, as the account and the card itself are clean and functional, with no issues whatsoever. So, it looks like I’ll have to wait until I can add it through Apple Pay.