It gives me an error message that says there is an issue with your payment method

Read this document about how to view your current payment types and add Apple ID payment methods on an Apple mobile device, a Mac, or a PC --> Add a payment method to your Apple ID - Apple Support

If an item appears in red then it is no longer working and you either need to replace it or get it working again. The latter may be more readily resolved by contacting your bank and see if there's a problem at their end. All Apple is doing is trying to ask the bank and either not getting a response or getting a negative one.

I had the same issue when the year ended and my card expired. Every time I tried to update the CC info, it said there was an issue with my payment method (not "declined" or "failed", just "an issue"). Here's what I did and it's not very scientific but it worked. First, I added my debit card to my account so at least there was a payment method on file (this is probably not a necessary step, but it's what I did). Then it occurred to me that since my original credit card was connected to my ApplePay, perhaps it hadn't updated there or it had and there was some kind of disconnect or glitch with Apple thinking there were two cards??? Anyway, I deleted my CC from Apple Pay, then re-entered and connected it to ApplePay, and finally, I returned to my Apple account | payment methods and entered the card info. It worked!! Good luck!