There's also no way to go to the wallet from the actual shortcut screen you most commonly use (the double-click power one)

Wait, what? Double-clicking will prompt for Face ID to open your default card for oayment, and from there you swipe down to see the stack — which I suppose is the screen you’re looking for.

But you cannot edit, add, or remove anything in this stack, and there's no way to go from it to the wallet. You have to close it, and open the actual wallet app which will show a slightly different view, and more items

You’re right, I never noticed!

This actually also explains why I couldn’t change my default card the other day - I must have been in that screen that opens from the button shortcut.