Walk me through it.

Why do you have all these steps to pay at a supermarket?

When I am here in the UK, I wave my phone over the card reader, it goes "Pling!" and that's my stuff paid for.

Of course, it's different elsewhere.

When I am over in Austria, I wave my phone over the card reader, it goes "Pling!" and that's my stuff paid for, but this time in Euros, at the going exchange rate.

You don't. As others have pointed out you can pay like normal. Even if you want to get Prime discounts all you need to do is have the card on your Amazon account. No scanning codes or typing in phone numbers is needed.

In the US, you also wave your phone over the card reader, it goes "Pling!" and that's your stuff paid for. The GP comment is not about paying (although it can do that too [1]), but rather about providing their Amazon account details for Amazon Prime discounts and other benefits.

A similar process is the case in the UK as well at Amazon Fresh stores, last I checked.

[1] https://www.amazon.com/gp/help/customer/display.html?nodeId=...