Unable to change my payment settings in Apple account or on my iPhone 13

Why not?

If you need to change or update your Apple Account payment method

(Also includes Mac, PC)

See this article for information about updating payment methods on various platforms (iPhone, Mac, etc.): If you need to change or update your Apple Account payment method - Apple Support

Here is how you update your payment method on an iPhone or iPad:

1. Open the Settings app.

2. Tap your name.

3. Tap Payment & Shipping (formerly Media & Purchases). You might be asked to sign in with your Apple ID.

4. Tap Add Payment Method, enter the new payment method, then tap Done.

5. Tap Edit.

6. Tap the red delete button next to the old payment method, then tap Delete.

Also note:

1) ”If you change your address, the credit or debit card information that you use with your Apple Account might be automatically updated by your financial institution, and you don't need to take action.”

2) “If there's an issue [such as you having a subscription or being a Family Sharing Organizer], add a new card first, then remove the old card."

If an app or feature on your device is not working, not appearing, or is restricted (grayed out), it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.

- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple Account is grayed out in Settings - Apple Support

Tap Settings > Screen Time > Content & Privacy > scroll to Allow Changes and turn on.

- If the device is managed (Settings > General > VPN & Device Management), contact the IT department that is doing the managing.

Use this link to check the status of Apple’s various services and servers —>

Apple - Support - System Status

To me it appears there are various server related issues. Although the App Store itself is working, some related servers appear to have an issue.Try again later when they have cleared.