Do you perhaps know how this message is prompted?
From the swipe down quick settings, or from the lock screen? Cause these can be easily edited and perhaps you could then forget about the app.
I’m wondering that it shows in the text “Google Pay” because it’s the old version of “Google Wallet”. You should check in your apps if Google Pay is installed and uninstall it.
If you are at this point in your settings, press the “three point menu” in the upper right corner and activate “show system apps” or similar naming. Usually the Google Wallet/Pay app is installed as a system app and can be listed like this, if it is installed.
I have Google Wallet installed on my FP4 and here are my observations
“Google Wallet” is shown in the list of all apps just like any other normal app, i.e. no need to explicitly select “show system apps”
when I open Google Wallet, it shows a similar hint but not identical; for me it’s “Überall mobil bezahlen, wo Google Pay akzeptiert wird” plus a button “Zahlungskarte hinzufügen”, i.e. the payment method’s name is “Google Pay”, no matter what the app to use it is called (or used to be called)
I didn’t install Google Wallet immediately when I got my FP4. But I have a vague recollection that I’ve also seen hints/notifications by the system from time to time trying to nudge me into using Google Wallet before I had it installed. That was maybe 2 or 3 years ago, so I don’t really remember how that looked like exactly and how often it appeared and if I had found a way to disable it.
Edit: so, yeah, I think this could very well be a not so subtle hint by Android to install Google Wallet and not a sign that it’s already installed without user interaction/consent.
Doesn’t mean I have a solution, though.
I still believe, that you are using the quick start button on the lock screen or something similar. Because your screen exactly shows what happens after using it without having wallet installed..