I've just encountered the same issue
Tried to resolve it by sideloading an older v8.11 apk (which works atm on my tablet) - downloaded it from https://www.apkmirror.com/apk/evernote-corporation/evernote/evernote-8-11-release/ (there's other versions available there as well).
However that didn't resolve the issue (still the same pop-up).
What did work was disabling google smart lock - rebooting the phone - and then manually entering my credentials again (aka not using any form of auto-fill in).
That logged me in correctly - after which I re-enabled smartlock & updated to the latest version in the store -> still being successfully logged in.