Unfortunately, that's the exact problem here: Google tried to force their Indian application internationally without exactly understanding the differences between different markets (big one is forced mobile number registration, which I understand is not a big deal in India but it's a significant friction in the US). For users outside of India, it is a mess compared to how Apple (and even Samsung at this point) does it.

Is this down through the old Google Pay app, not through the newer Wallet app? I use "Google Pay", as in the payment processor, every day, but it is being done through the wallet app.

It is the Google Pay app. The Google Wallet app is separate and (at least in India) do not have payment functionality.

Edited to add: actually the popular app in India is GPay which I think is different from the older Google Pay.

Google's payment apps are very confusing.