it do not auto transfer cards to the watch you have to add them separately
what AI Says
"You can add a credit or debit card to your Apple Watch using the Apple Support Guide via your paired iPhone or directly on the watch itself.
Method 1: Using Your Paired iPhone (Recommended)
- Open the Apple Watch app on your iPhone. [1]
- Go to the My Watch tab and select Wallet & Apple Pay. [1]
- Tap Add Card, then tap Debit or Credit Card (or choose from Cards Found For You). [1]
- Tap Continue and scan your card or enter the details manually. [1]
- Follow any verification steps required by your bank. [1]
Method 2: Directly on Your Apple Watch
- Open the Wallet app on your Apple Watch.
- Tap the Add Card option (or the + icon).
- Select Debit or Credit Card and follow the instructions on the screen. [1]
If you want, tell me:
- What bank or card issuer are you trying to add?
- Are you running into a specific error message during setup?
I can help you troubleshoot or complete the process."
more
Apple Watch User Guide - Apple Support (AL)
even more
apple watch add credit card - Google-