Everytime I click on payment method it just says “we have run into a problem”

Try this link Change, add, or remove Apple ID payment methods https://support.apple.com/en-us/HT201266?

See especially If you can't edit your payment information:

"Try updating to the latest version of iOS or iPadOS or macOS.

If you have subscriptions, have an unpaid balance, or share purchases with your Family Sharing group, you can't remove all payment information. Get help if you want to use no payment method with your Apple ID."

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

If necessary, contact iTunes Support. See the Apple Support articles below for contact information.   

iTunes Support – world wide 

Apple Support schedule phone call       

Azpul243 Said:

“Payment method: I have been trying to change my card on my Apple ID for a couple of weeks now because it keeps loading up my old one and everytime I click on payment method it’s just says “ we have run into a problem”

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Approve this Card Usage:

If you have a secure bank, then, for security purposes, this card activity may be being denied. So, contact your financial institution (i.e. bank) and see if you need to approve of this to go through.