Actually, it seems there may already be a workaround. It requires configuring the Google service under the “Access your users’ Google Drive files” (despite only wanting to use it for the Users login:
I’m trying it out on my own app to confirm whether it works. (It’s not working yet, but Google is telling me I need to wait for them to verify my application, which may take a few days. Maybe it will work then.)
It takes some work (and a link to your app’s privacy policy) to get Google’s permission, which lines up with @ianb’s point.
update: Pre-verification, the Google auth screen currently lists “anvil.works” as the site but shows no logo and has replaced the privacy policy link near the bottom with the link I specified to Google.