I did that, too. But I have another issue: I don’t see anything about Play Integrity API in any App-info.
My issues with the SC app are a bit different: I can login, but only if the app is not (!) running when I click on login in the browser. So, I have to open the app only after the browser demands the 2FA. Otherwise, nothing happens inside the app. For other things that require 2FA, it just doesn’t work. The browser waits for authentification via the app, but the app doesn’t react in any way.
I never saw any pop-up about the OS being modified.