How can I update payment method on Apple Pay?

The App Store and iTunes Store, do not use Apple Pay at all.

To add your payment method to your account for those services, follow the steps in the support document linked below.

click here ➜ Add a payment method to your Apple Account - Apple Support

What is asking you to log in to the Pay Pal account?

Adding a card to your Apple Account has no relation to Pay Pal.

If Pay Pal was added as a payment method, not may be asking you to update it, but that should have no bearing on adding a new payment method.

Please follow the steps in the link below.

click here ➜ Add a payment method to your Apple Account - Apple Support

Unless there's some other restriction in place, it should allow you to add additional payment methods.

Is Screen Time active?

Do you have a school or office email account or profile installed?

Is your Apple ID part of a Family Sharing group?

If Screen time is active, some parental restriction may be in play. You would need to disable any Parental restrictions in Screen Time.

If you have school or email account or profile it may be restricting adding new payment methods. You would need to talk to them to get it enabled.

If you are part of Family Sharing, then if purchase sharing is turned on, adding payment methods for individual members is disabled. You would need other leave Family Sharing to be able to add a new payment method.

Don't click on PayPal, click on "Add Payment Method" below that.