It is possible to scavenge the NFC antenna/chip from an Oyster card or indeed any other card, which the author alludes to in their video. There are details floating around on how to do it, by dissolving the card in acetone.

However, the relevant authorities might take a dim view of repurposing the transit card in this manner and probably have certain restrictions in place, to deter people from defacing their property. On another note, the author is using a NTAG213 on the watches sold via the shop and Oyster is Mifare, from what I can remember. There might be issues with response times regarding the proximity to the reader, if you wanted to experiment.

I follow someone on twitter who explained how to do this at one point, using a Caltrain Clipper card, and put it in a resin ring :)

I could dig that up if it’s helpful but in general I think it’s pretty straight forward, just some risk of destruction :)

Oh, thank you so much ! I'll guess I'll be adding another F91W to my collection :)

It says: "Be aware, this particular NFC chip is NOT compatible with tap-to-pay."

hum... That's sad. It's almost there ! Does tap-to-pay require specific maker certificates ?

Tap to pay requires you to extract the certificates & private keys of a real card. You can write (or license) an EMV applet for any JavaCard or similar smartcard that allows you to run arbitrary code, but without the keys associated with a valid payment card it won't do anything.