Many thanks for the response ... though I'm still somewhat confused, as I'm not sure whether you are agreeing with what I said ... or not.
When you say ".. install the Suica card.." do you mean the app? I am familiar with adding a virtual Suica card via the (Japanese language) app. I assume that can only be done on the phone and not directly on the watch - is that correct? In creating that first card on the phone, you would transfer it to the wallet on the watch. That done, you would then add another card to the phone. If that is not the correct sequence, please clarify.
Yes the Suica app is the central point for both the watch and the phone. You just issue 2 virtual suica cards within the app and fund them and then add one to the phone's wallet and one to the watche's wallet.
Simple as that.
Once 2 cards are in the app you will find you can swipe between the 2 cards to manage them as appropriate.