All these things are controlled, not by the card, but by the bank’s computers.
When you verify your new card with your pin, your pin, encrypted both by your card and by the terminal, is sent to the bank’s computers for verification. So they know, and mark their record of the card as authorised to do contactless transactions.
Contactless transactions, too, are sent to the bank for verification.
Similarly, the contactless limit is also managed by the bank’s computers. The terminal send the purchase request, with a signature produced by the card’s chip, to the bank. The bank then sends back a reply that indicates whether the pin is required.
Your bank card doesn’t know much at all. I’ve never looked into this in depth, but in theory all it has to know is its number. Everything else is done between the card system and the bank.
Say you tap your card at a store.
Card: Hiii! I’m card number XXXXXXXXX!
Card reader: *rings Visa* ‘ey yo, I got this card here, number so-and-so. Is he legit? Also, he tapped.
Visa: Yup, he’s legit. Under the limit, too, so just tell him it’s accepted and I’ll note it down.
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