Could you reveal part of the private key (so that you have some authenticity) then have some kind of gadget that sends a message on chain to keep a record that the card has been opened, or something like that?
Partial revealing of private key in public would reduce security and increase chances of someone stealing your coins, so I wouldn't do that.
Is it possible to have bitcoin notes in that case, with the denomination (e.g 50 sats), the private and the public key, printed on the note, and each note have it's own wallet ID?
There are several types of Bitcoin notes already, and I even saw one project is working on DIY BTC notes that people could print in their homes.
I don't know if we could add 50 sats that you can't spent for anything today, and it would be very stupid to print something with value of 1 sat being around $0.00016,and 50 sats = 0.00840081.
Alternative for Bitcoin notes are cards that can be used like cash are Satodime, Satscard, and maybe few more.