when you get an offer to UPGRADE an amex product to one that has a higher annual fee and better benefits, AMEX does NOT do a hard pull, which is what you normally get when you apply for a credit card

instead, they do a SOFT pull, which means they get (possibly limited) information to check that you don't have any delinquencies and that's it

it does not negatively affect your credit score and shouldn't negatively affect your amex CC. you either qualify for the upgrade or do not, no retribution from AMEX