As detailed in Experience Cloud Profile Details article that you can select the fields you want to show in the view.

The permissions of these fields will be based on the profile and permission sets assigned to the experience cloud user. Meaning if the user have read permission for a field then it will visible in read only mode, if read and edit then field will be available for edit as well.

Users with "Payments2Us Site users" will have edit permission to most of the contact fields that are part of Payments2Us package. IN order to show these fields as read only fields, create a formula field and add that formula field instead of showing the actual field.

Example, if you want to show "Membership No."(AAkPay__Membership_No__c) field on the profile update view in read only mode then create a custom formula field that evaluates to the Membership No. field of Payments2Us and add that field in the fieldset.