I know. I am entertaining the OP's exercise in how one might make a thinner device. CR2032s are more than 4 times as thick as a credit card, even without a socket or a housing.
The thinnest commonly available coin cells are 1.2mm thick, which is better, but still will require a creative interpretation of "credit card size".
The thinnest commonly available coin cells are 1.2mm thick, which is better, but still will require a creative interpretation of "credit card size".
An ISO credit card is 0.76mm thick.