Your issue(s) involve several different settings and you still may not be able to fully resolve the issue(s).
1) Banks may restrict the region you can add the card. If you’re in a different region, from the bank, you may not be able to add the card to your Wallet. Apple ID is associated with a region and your Apple device is associated with a region.
2) Changing regions on your device could possibly disable other cards. Some countries restrict their cards to specific regions. It may depend on the type of card you have, debit, credit or prepaid debit etc.
3) Changing regions to other regions to use different App Store, iTunes store, etc, store may require you to spend funds in your Apple Account/Apple Gift Card.
4) Verifying a credit/debit card may not be supported by the issuing bank.
I can probably think of another 5 or 6 issues that could prevent you switching regions and verifying your credit card.
I’m happy to start troubleshooting with you, but the next step would be to talk to somebody at the bank that issued the card and verifying with their support team that the card can be added when you are outside their region. Will they use email, voice or Text to verify and will they do it to a country in another region?
Next question is will you need to change region on your device? If you have to change region, do you have issues with funds in another region Apple Store?
Resolve that and you can follow your banks guidance on verifying your card. This may require you to contact a higher level of support at your bank to verify this can be done.
I hope this helps.