I am unable to update Payment Methods linked to my Apple ID.

If any of the six options listed below is true, selecting "None" as a payment method won't appear, and you cannot remove an expired or lost card. In such cases, providing billing information is mandatory.

The "None" option will not appear...

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing

Based on your country of residence and country you have selected under your Apple ID --> Payment methods that you can use with your Apple ID - Apple ...

Have you a Debit/Credit card issued to you that is valid internationally and from the same Country / Region as your Apple ID?

Know it here --> If your payment method is declined in the App Store or iTunes ...

Check the following

1. The payment method that you are adding is of the same country as that of App Store Country on your iPhone
2. You have a valid payment plan debit/credit card from an authorized bank from the same country
3. Payment methods that you can use with your Apple ID - Apple Support
4. Learn more about family purchases and payments.
5. Please check if your Debit/Credit card is valid internationally

If you can't download, make purchases, or update apps, including free apps, you must update your payment method or add a new one. If you verified that a payment method is available in your country or region and you're still having trouble, learn more.

You have to provide the "why". We cannot see your accounts or what is being displayed on your device.

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