Google wallet in smart watches

I have Google Wallet in my Pixel 6 phone as well as in my Fitbit Charge 5. I have two credit cards working flawlessly with my phone: Costco Visa and Delta Amex. However, I can not get the Costco Visa work in my Fitbit at all. Previously I had a Pixel Watch and all cards that I had in my phone Google Wallet worked in it. Why not in Fitbit? Both watches and the phone are all made by Google after all.