The banks that issue the cards require that their cards, the device and the account owner reverify the cards for each device they are added to. Syncing the cards through iCloud is for the transactional data (recent payments and transactions). This restriction is an anti fraud precaution. It’s simple to fix my just using the Watch app on your iPhone and entering the card details required by the bank.
Data syncing can be slow and especially if the Apple Watch has just recently been paired with your iPhone. Syncing generally happens at night and while the watch is locked and on its charger. If you’ve had the Watch for several weeks or months and still not synced, it probably needs to be re-paired with your iPhone.