I am unable to add my new Apple Card to my iPhone Wallet

1. Are you saying you got a physical card? If so, you would have had to order it from the Wallet app and by extensions the Apple Card should have already been there for you to be able to order it.
2. If you did not get a physical card, then what did you get exactly?
3. The Apple Card's number can be found the following the steps in the support document you posted from.
4. The Apple Card is tied to the Apple ID that was used to Apply for it. If used a different Apple ID on a different device to apply for it, you won't be able to add it to the iPhone.

Please explain exactly what you did and what you received.

Is your iPhone region set to the U.S.? Settings->General->Language & Region->Region

If it is, try restarting your iPhone, connecting to Wi-Fi and trying again.

You're welcome. Glad it worked out.