Yes. iOS is at the most recent update.
This is the Apple Card (credit card). There are three additional users on this card (my wife and children). The card works perfectly fine on other devices. The only one experiencing this problem is my wife, on her iPhone.
I can identify only two possibly significant differences between the three of us who use the card regularly and normally, without any issues, and my wife, who is experiencing this problem. The three of us have iPhones with Face ID (two iPhones 16, one iPhone 13), while my wife as the SE with Touch ID, and she never set up the Touch ID, always using passcode to unlock.
The other possible wrinkle (although I doubt this has any bearing on this), my wife doesn't have a Social Security number, which usually adds an additional layer of hassle when dealing with banks and credit card issuers. In the case of Apple Card, she cannot set up Apple Cash (which requires SSN), so the cashback that she accumulates cannot be used, and we periodically have to call Goldman-Sachs (Apple Card support, to be precise) and request them to manually transfer that money to her bank account. I can't imagine how this would affect the behaviour of the Wallet app (or Settings). I could possibly see how lack of Touch ID setting might be an issue, if a bug was introduced into the Card Details screen authentication requirements at some recent update, that now exclusively requires biometric authentication, and doesn't allow the passcode unlocking. In the past, this worked pefectly fine with the passcode; the problem started appearing rather recently (a few months or so).