Do you happen to know where in Japan your friend got that from? I know someone (including myself) who would love that as a gift.
I found what appears to be an actual ID card you order for your cat (1 - Japanese), (2 - translated). It even has a place to specify where they like to be petted!
May resolve GP's problem as it has a spot for the birthday.
1: https://pawmy.jp/product/cat-license/
2: https://pawmy-jp.translate.goog/product/cat-license/?_x_tr_s...
I would show bouncers who never thought it funny. My fave was one looked all over it and said "What?? Theres no birthday!"